Composite bearing load calculation method considering ferrule deformation

Abstract

The invention discloses a composite bearing load calculation method considering ferrule deformation. The composite bearing load calculation method comprises the following steps: step 1, enabling m rolling body rows to be equivalent to springs capable of bearing axial load, radial load and torque; constructing a non-rigid shaft system stress schematic diagram of the composite bearing; step 2, calculating the acting load on each inner ring according to the deformation of the mandrel; 3, calculating the Hertz contact deformation of the rigid ferrule under the loading condition; 4, calculating the contact deformation generated by the deformation of the ferrule; 5, solving the total radial deformation of the raceway contact considering the deformation of the ferrule; 6, calculating the load of the rolling body at the position by using the total deformation of the rolling body and the inner and outer ferrules; and 7, verifying the resultant force of each row of rolling bodies and the reliability of the external load borne by the bearing. According to the method, the acting load of each row of rolling bodies of the composite bearing is calculated, and load analysis is performed on the composite bearing under the condition of considering the deformation of the ferrule, so that a more accurate calculation result is obtained and applied to bearing design.

Description

Technical Field

[0001] The invention relates to the technical field of rolling composite bearing load calculation, in particular to a composite bearing load calculation method taking into account ring deformation. Background Art

[0002] Composite bearings are one-piece bearings, mainly composed of a common outer ring, rolling elements and multiple separate inner rings. Composite bearings are equivalent to the combination of ball bearings and roller bearings, so they can withstand radial loads, axial loads and moment loads at the same time. Compared with ordinary bearings, composite bearings have high structural integration, complex loads, and high manufacturing and assembly requirements. However, in specific areas, such as the bearing under the rotating early warning radar antenna cover, it is necessary to use a high-composite bearing to better meet various performance requirements and ensure the stability and reliability of the machine.

[0003] A certain type of early warning aircraft carries an ellipsoidal rotatable early warning radar antenna cover (referred to as the rotatable cover), which is fixed on the skirt section of the bracket through upper and lower bearings. The rotating upper and lower bearings are key components to achieve its rotation and load transmission. At present, my country's lower bearing adopts a combination of double-row spherical roller bearings + four-point angular contact ball bearings, but the design life of the lower bearing assembly is low, and there is a large gap from the required flight life. To address this problem, a high-composite bearing composed of a bearing seat, a full-fill rolling bearing (full-fill double-row angular contact ball bearings and cylindrical roller bearings), a self-aligning self-lubricating spherical bearing, a retaining ring, etc. is proposed. Due to the complex structure, it is very difficult to perform static analysis on it. From the existing technical methods, it is difficult to accurately express the load analysis of the high-composite bearing when considering the deformation of the thin-walled ring. Summary of the invention

[0004] The purpose of the present invention is to provide a composite bearing load calculation method taking into account the deformation of the ring, and to calculate the load of the composite bearing under the condition of taking into account the stress deformation of the thin-walled ring, so as to obtain more accurate calculation results and apply them to bearing design.

[0005] The solution implemented by the present invention to solve the above-mentioned problem is: a method for calculating the load of a composite bearing taking into account the deformation of the ferrule, wherein the composite bearing comprises m inner rings, a common outer ring and m rolling element rows arranged between each inner ring and the outer ring, each row of rolling elements corresponding to an independent inner ring, and the rolling elements are steel balls or rollers, comprising the following steps: Step 1: Equivalent the rolling element to a spring capable of bearing axial load, radial load and torque; construct a force diagram of the non-rigid shaft system of the composite bearing, and define F n is the reaction load at the bearing support position in the nth column from left to right; l n It is the distance from the center section of the nth row of rolling elements to the center section of the next row of rolling elements; is the kth load from left to right acting on the center section (right side) of the nth row of rolling elements; For the load The moment at the location; Step 2: Based on the force diagram constructed in step 1, calculate the load acting on each inner ring according to the deformation of the core shaft; Step 3: Calculate the Hertz contact deformation under the condition of rigid ring loading; Step 4: Calculate the contact deformation caused by the deformation of the ferrule; Step 5: Calculate the total radial deformation of the raceway contact considering the deformation of the ring; Step 6: Use the total deformation of the rolling element and the inner and outer rings δ i Calculate the rolling element load Q at this position i . As a preferred solution, the specific process of step 2 is as follows: The rotation angle equation and deflection equation at the center section of each row of rolling elements in the two-bearing system are solved by the static balance of the hyperstatic system and the integral method: Where: F1, F2 are the loads acting at the bearing support, P is the external load, M1, M2 are the moment loads caused by the flexible shaft in each row of bearings, l is the distance between the center sections of the two rows of rolling elements, a is the distance between the position of the external load P and the center section of the first row of rolling elements; Where: EI represents the bending stiffness of the mandrel, θ, y represent the rotation angle and deflection along the x (center axis of the mandrel) direction, which is also the deformation of the mandrel; The above equation is obtained by the boundary conditions x = 0, y = δ r1 , θ=θ1; when x=l, y=δ r2 , θ=θ2; and x=a, there is a unique θ and δ, and there are multiple loads or couples acting between the center sections of the two rows of bearings at the same time, then the superposition principle can be applied to obtain the force and moment loads acting on the inner ring: Decomposing the loads F2 and M2 in the above formula into F′2, F″2, M′2, M″2, F′2+F″2=F2, M′2-M″2=M2, the loads on the three-row rolling element bearing can be obtained: This method can be used to calculate the reaction force and torque of each row of bearings in a multi-row rolling element composite bearing system: When the span of each row of rolling elements in the bearing is very small, the radial displacement of the bearing will determine the load distribution between the bearings, which can be obtained from the similar triangle relationship: As a preferred solution, in step 3, when the rolling element is a roller, the specific process is as follows: In order to consider the influence of roller inclination on the contact state, the slice discretization is performed along the roller generatrix, and the thickness of a single slice is 2ω=l e / N(l e is the effective length of the roller, N represents the number of discrete slices), according to the Hertz contact theory, the contact deformation between the roller slice unit and the raceway is: in Where: l e is the effective length of the roller, 1 λ is the distance from the slice center to the left end of the roller, is the axial displacement caused by the inclination of the roller center, c λ is the modification amount of the roller at the center of the slice unit, is the radial clearance between the roller and the raceway; When the rolling element is a ball, the specific process is as follows: Assuming that the outer ring is fixed, the distance between the inner and outer groove curvature centers at any position before the bearing is loaded is A, A = (f i +f e -1)D w , the total contact deformation of the steel ball and the inner and outer rings at any position ψ after the bearing is loaded is equal to the center distance S of the groove curvature after displacement ψ The difference from the original center distance A, that is: δ ψ =S ψ -A S ψ =[(Asinα 0 +δ a +R i θcosψ-u a ) 2 +(Acosα 0 +δ r cosψ-u r ) 2 ] 1 / 2 As a preferred solution, the specific process of step 4 is as follows: Bending deformation of bearing ring According to the plane bending theory of thin-walled ring, the differential equation of radial flexural deformation of the ring at any azimuth angle φ is: The thin-walled ring produces a small deflection deformation under the action of external force. The displacement of any point on the center line of the ring can be decomposed into radial displacement w and tangential displacement v. The trigonometric series expressions of radial displacement and tangential displacement are: The virtual displacement of the force in the radial direction and the work done by the external force can be expressed as: According to the virtual displacement principle, the change in the strain energy of the ring is equal to the work done by the external force: Radial displacement ω caused by radial force p and the tangential displacement ω caused by the tangential force t for: Radial deformation of the outer ringω po and ω to And the radial deformation of the inner ring ω pi and ω ti , then any azimuth Contact deformation caused by ring deformation in the middle and lower part: Among them I o and I i are the bending moments of inertia of the outer and inner rings respectively; Represent the radial force and tangential force of the outer ring and inner ring respectively. As a preferred solution, in step 5, the specific calculation process of the total radial deformation of the raceway contact considering the deformation of the ring is as follows: Total radial deformation of the rolling element at any position for: As a preferred solution, in step 6, the total deformation of the rolling element and the inner and outer rings δ i Calculate the rolling element load Q at this position i : For roller bearings: δ i =K r Q i 0.9 or: For ball bearings: or: Where K r , K b is a coefficient that is independent of the rolling element load. As a preferred solution, a verification step of the resultant force of each row of rolling elements and the external load on the bearing is also included, and the verification is performed by the following formula:

[0006] Beneficial effects: 1. The present invention considers the load distribution of each row of rolling elements in the composite bearing, and then simplifies it by performing load analysis on single-row ball and single-row roller bearings, and establishing a static model of the composite bearing. 2. The present invention is based on the analysis of rigid rings. The contact deformation of the rigid rings under loading is calculated based on Hertz contact. Then, the contact deformation caused by the ring deformation is calculated according to the virtual displacement principle. Then, the total radial deformation of the raceway contact considering the ring deformation is obtained. Then, the load of each row of rolling elements can be analyzed to obtain more accurate calculation results and apply them to bearing design. 3. The analysis process and processing method of the composite bearing of the present invention can provide a reference for other similar bearing research. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings based on the basic principles described in the present invention without paying any creative work.

[0008] Figure 1 It is a schematic diagram of the general statics model of composite bearings; Figure 2 It is a schematic diagram of the analysis of a three-row rolling element composite bearing; Figure 3 It is a schematic diagram of the effect of ring deformation on raceway contact deformation; Figure 4 Load distribution diagram of the first ball bearing before and after considering the ring deformation; Figure 5 This is the load distribution diagram of the middle row cylindrical roller bearing before and after considering the ring deformation; Figure 6 This is the load distribution diagram of the right-row ball bearing before and after considering the ring deformation. DETAILED DESCRIPTION A load calculation method for composite bearings considering ring deformation is shown below. Figure 1-6, the implementation of the present invention is specifically described. The composite bearing described in this scheme includes m inner rings, a common outer ring and m rolling element rows arranged between each inner ring and the outer ring, each row of rolling elements corresponds to an independent inner ring, and the rolling elements are steel balls or rollers. The method includes the following steps:

[0009] Step 1: Figure 1 As shown, the rolling element is equivalent to a spring that can withstand axial load, radial load and torque; a force diagram of a non-rigid shaft system of a composite bearing is constructed, and F is defined. n is the reaction load at the bearing support position in the nth column from left to right; l n It is the distance from the center section of the nth row of rolling elements to the center section of the next row of rolling elements; is the kth load from left to right acting on the center section (right side) of the nth row of rolling elements; For the load The moment at the location.

[0010] Step 2: Calculate the load on each inner ring according to the deformation of the mandrel; The rotation angle equation and deflection equation at the center section of each row of rolling elements in the two-bearing system are solved by the static balance of the hyperstatic system and the integral method: Where: F1, F2 are the acting loads at the bearing support position, P is the acting external load, M1, M2 are the moment loads caused by the flexible shaft of each row of bearings, l is the distance between the center sections of the two rows of rolling elements, a is the distance between the position of the external load P and the center section of the first row of rolling elements, EI represents the bending stiffness of the mandrel, θ, y represent the rotation angle and deflection along the x (center axis of the mandrel) direction, which is also the deformation of the mandrel; The above equation is obtained by the boundary conditions x = 0, y = δ r1 , θ=θ1; when x=l, y=δ r2 , θ=θ2; and x=a, there is a unique θ and δ, and there are multiple loads or couples acting between the center sections of the two rows of bearings at the same time, then the superposition principle can be applied to obtain the force and moment loads acting on the inner ring: Decomposing the loads F2 and M2 in the above formula into F2', F2", M'2, M2", F2'+F2"=F2, M'2-M2"=M2, the loads on the three-row rolling element bearing can be obtained: This method can be used to calculate the reaction force and torque of each row of bearings in a multi-row rolling element composite bearing system: When the span of each row of rolling elements in the bearing is very small, the radial displacement of the bearing will determine the load distribution between the bearings, which can be obtained from the similar triangle relationship:

[0011] Step 3: Calculate the Hertz contact deformation under the condition of rigid ring loading; When analyzing the roller array, in order to consider the influence of roller inclination on the contact state, the slices are discretized along the roller generatrix, and the thickness of a single slice is 2ω=l e / N(l e is the effective length of the roller, N represents the number of discrete slices), according to the Hertz contact theory, the contact deformation between the roller slice unit and the raceway is: in Where: l e is the effective length of the roller, 1 λ is the distance from the slice center to the left end of the roller, is the axial displacement caused by the inclination of the roller center, c λ is the modification amount of the roller at the center of the slice unit, is the radial clearance between the roller and the raceway; When analyzing the steel ball row, it is assumed that the outer ring is fixed and the distance between the inner and outer groove curvature centers at any position before the bearing is loaded is A, A = (f i +f e -1)D w , the total contact deformation of the steel ball and the inner and outer rings at any position ψ after the bearing is loaded is equal to the center distance S of the groove curvature after displacement ψ The difference from the original center distance A, that is: δ ψ =S ψ -A S ψ =[(Asinα 0 +δ a +R i θcosψ-u a ) 2 +(Acosα 0 +δ r cosψ-u r ) 2 ] 1 / 2

[0012] Step 4: Calculate the contact deformation caused by the deformation of the ferrule; Bending deformation of bearing ring According to the plane bending theory of thin-walled ring, the differential equation of radial flexural deformation of the ring at any azimuth angle φ is: The thin-walled ring produces a small deflection deformation under the action of external force. The displacement of any point on the center line of the ring can be decomposed into radial displacement w and tangential displacement v. The trigonometric series expressions of radial displacement and tangential displacement are: The virtual displacement of the force in the radial direction and the work done by the external force can be expressed as: According to the virtual displacement principle, the change in the strain energy of the ring is equal to the work done by the external force: Radial displacement ω caused by radial force p and the tangential displacement ω caused by the tangential force t for: Radial deformation of the outer ringω po and ω to And the radial deformation of the inner ring ω pi and ω ti , then any azimuth Contact deformation caused by ring deformation in the middle and lower part: Among them I o and I i are the bending moments of inertia of the outer and inner rings respectively; Represent the radial force and tangential force of the outer ring and inner ring respectively.

[0013] Step 5: Calculate the total radial deformation of the raceway contact considering the deformation of the ring; Total radial deformation of the rolling element at any position for:

[0014] Step 6: Use the total deformation of the rolling element and the inner and outer rings δ i Calculate the rolling element load Q at this position i : For roller bearings: δ i =K r Q i 0.9 or: For ball bearings: or: Where K r , K b is a coefficient that is independent of the rolling element load.

[0015] Step 7: Verify the reliability of the combined force of each row of rolling elements and the external load on the bearing:

[0016] Test verification: Taking a three-row rolling element composite bearing with two rows of balls and a row of rollers in the middle as an example, the load distribution inside the bearing under certain working conditions is calculated based on the static model established by the present invention. The bearing parameters are as follows: As shown in Table 1 and Table 2.

[0017] A 300KN radial load is applied to the center section of the roller row. Finite element and programming are used to calculate and analyze the bearing load for both the case where the ring deformation is not considered and the case where the ring deformation is considered. The verification results are as follows: Figure 4-6 As shown: When the left (right) row bearings do not consider the deformation of the ring, the No. 1 rolling element bears a maximum load of 7123.25N. When the deformation of the ring is considered, the No. 2 rolling element bears a maximum load of 7107.76N. The loads of the No. 2-14 rolling elements increase slightly, and the loads of the No. 67-78 rolling elements decrease. When the ring deformation is not considered, the No. 1 rolling element of the middle row bearings bears a maximum load of 5865.29N. When the ring deformation is considered, the No. 2 rolling element bears a maximum load of 5846.36N. The loads of the No. 2-21 rolling elements increase slightly, and the loads of the No. 62-80 rolling elements decrease. Therefore, it can be known that considering the deformation of the ring can change the position of the maximum load of the rolling element and reduce the maximum load of the rolling element. The overall load of the rolling element in the bearing changes. The influence of the ring deformation cannot be ignored when performing load analysis on thin-walled ring bearings.

[0018] It should be noted that although the scheme described in the present invention is described through the above-mentioned embodiments, there may be other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and deformations to the present invention, but these changes and deformations should all fall within the scope of protection of the appended claims of the present invention and their equivalents.

Claims

1. A method for calculating the load of a composite bearing taking into account the deformation of a ferrule, wherein the composite bearing comprises m inner rings, a common outer ring, and m rolling element rows arranged between each inner ring and the outer ring, wherein each row of rolling elements corresponds to an independent inner ring, and wherein: The following steps are involved: Step 1: Equivalent the m rolling element rows to springs capable of bearing axial load, radial load and torque; construct a force diagram of the non-rigid shaft system of the composite bearing, and define F n is the reaction load at the bearing support position in the nth column from left to right; l n It is the distance from the center section of the nth row of rolling elements to the center section of the next row of rolling elements; is the kth load from left to right acting on the right side of the center section of the nth row of rolling elements; For the load The moment at the location; Step 2: Based on the force diagram constructed in step 1, calculate the load acting on each inner ring according to the deformation of the core shaft; Step 3: Calculate the Hertz contact deformation under the condition of rigid ring loading; Step 4: Calculate the contact deformation caused by the deformation of the ferrule; Step 5: Calculate the total radial deformation of the raceway contact considering the deformation of the ring; Step 6: Use the total deformation of the rolling element and the inner and outer rings δ i Calculate the rolling element load Q at this position i .

2. A composite bearing load calculation method considering ring deformation according to claim 1, characterized in that: The specific process of step 2 is as follows: The rotation angle equation and deflection equation at the center section of each row of rolling elements in the two-bearing system are solved by the static balance of the hyperstatic system and the integral method: -l 2 (3x+3a-2l)+6xla]}+δ a -θ2(l-x) Where: F1, F2 are the loads acting at the bearing support, P is the external load, M1, M2 are the moment loads caused by the flexible shaft of each row of bearings, l is the distance between the center sections of the two rows of rolling elements, a is the distance between the position of the external load P and the center section of the first row of rolling elements, EI represents the bending stiffness of the mandrel, θ, y represent the rotation angle and deflection along the x direction, which is also the deformation of the mandrel; The above equation is obtained by the boundary conditions x = 0, y = δ r1 , θ=θ1; when x=l, y=δ r2 , θ=θ2; and x=a, there is a unique θ and δ, and there are multiple loads or couples acting between the center sections of the two rows of bearings at the same time, then the superposition principle can be applied to obtain the force and moment loads acting on the inner ring: Decompose the loads F2 and M2 in the above formula into F2', F2", M'2, M2", and F2'+F2"=F2, M'2-M2"=M2, then the loads on the three-row rolling element bearing can be obtained: This method can be used to calculate the reaction force and torque of each row of bearings in a multi-row rolling element composite bearing system: When the span of each row of rolling elements in the bearing is very small, the radial displacement of the bearing will determine the load distribution between the bearings, which can be obtained from the similar triangle relationship:

3. A composite bearing load calculation method considering ring deformation according to claim 2, characterized in that: In step 3, when the rolling element is a roller, the specific process is as follows: When analyzing the roller array, in order to consider the influence of roller inclination on the contact state, the slices are discretized along the roller generatrix, and the thickness of a single slice is 2ω=l e / N, where l e is the effective length of the roller, N represents the number of discrete slices. According to the Hertz contact theory, the contact deformation between the roller slice unit and the raceway is: in Where: l e is the effective length of the roller, 1 λ is the distance from the slice center to the left end of the roller, is the axial displacement caused by the inclination of the roller center, c λ is the modification amount of the roller at the center of the slice unit, It is the radial clearance between the roller and the raceway.

4. A composite bearing load calculation method considering ring deformation according to claim 2, characterized in that: In step 3, when the rolling body is a ball, the specific process is as follows: When analyzing the steel ball row, it is assumed that the outer ring is fixed and the distance between the inner and outer groove curvature centers at any position before the bearing is loaded is A, A = (f i +f e -1)D w , the total contact deformation of the steel ball and the inner and outer rings at any position ψ after the bearing is loaded is equal to the center distance S of the groove curvature after displacement ψ The difference from the original center distance A, that is: δ ψ =S ψ -A 5. A composite bearing load calculation method considering ring deformation according to claim 3 or 4, characterized in that: In the step 4, the specific calculation process is as follows: Bending deformation of bearing ring According to the plane bending theory of thin-walled ring, the differential equation of radial flexural deformation of the ring at any azimuth angle φ is: The thin-walled ring produces a small deflection deformation under the action of external force. The displacement of any point on the center line of the ring can be decomposed into radial displacement w and tangential displacement v. The trigonometric series expressions of radial displacement and tangential displacement are: The virtual displacement of the force in the radial direction and the work done by the external force can be expressed as: According to the virtual displacement principle, the change in the strain energy of the ring is equal to the work done by the external force: Radial displacement ω caused by radial force p and the tangential displacement ω caused by the tangential force t for: Radial deformation of the outer ringω po and ω to And the radial deformation of the inner ring ω pi and ω ti , then any azimuth Contact deformation caused by ring deformation in the middle and lower part: Among them I o and I i are the bending moments of inertia of the outer and inner rings respectively; Represent the radial force and tangential force of the outer ring and inner ring respectively.

6. A composite bearing load calculation method considering ring deformation according to claim 5, characterized in that: In step 5, the specific calculation process is as follows: the total radial deformation of the rolling element at any position for:

7. A composite bearing load calculation method considering ring deformation according to claim 6, characterized in that: In step 6, the specific calculation process is as follows: For roller bearings: δ i =K r Q i 0.9 or: For ball bearings: or: Where K r , K b is a coefficient that is independent of the rolling element load.

8. A composite bearing load calculation method considering ring deformation according to any one of claims 1 to 7, characterized in that: It also includes a verification step for the resultant force of each row of rolling elements and the external load on the bearing, which is verified by the following formula:

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