Small-swing-angle wear life prediction method and parameter optimization method for ball bearing of machine body

Abstract

The invention discloses a machine body ball bearing small swing angle wear life prediction method and a parameter optimization method, and relates to the machine body swing bearing wear life calculation field, and the method comprises the following steps: defining a bearing critical swing angle, calculating the slip speed of a steel ball relative to an inner ring channel and the slip speed of an outer ring channel, and building a contact pressure calculation model; the method comprises the following steps: acquiring a slip speed, calculating contact pressure, establishing a wear depth calculation model between a steel ball and a channel in combination with the slip speed and the contact pressure, establishing a wear life prediction method under a small swing angle working condition of a machine body ball bearing based on the wear depth calculation model, executing the wear life prediction method, and outputting the predicted wear life; based on the wear life prediction method, working condition parameter optimization is realized by drawing an equal wear life curve graph. The method solves the problems that the wear life of the bearing cannot be quantitatively evaluated under the small-swing-angle working condition and the swing parameters are lack of optimal basis.

Description

Technical Field

[0001] This invention relates to the field of calculating the wear life of machine body swing bearings, and particularly to a method for predicting the wear life of machine body ball bearings at small swing angles and a method for optimizing parameters. Background Technology

[0002] Airframe ball bearings are core connecting components in the airframe structure of large aircraft, widely used in critical parts such as landing gear, rudder, flaps, slats, tail, ailerons, spoilers, doors, engine mounts, mounting surfaces, and aircraft control systems, essentially serving as the "mechanical joints" of the aircraft. As a basic functional component, airframe ball bearings primarily achieve pitch, yaw, and attitude adjustments through small-angle reciprocating oscillations or low-speed rotations. Their motion characteristics manifest as periodic oscillations around a central position within a finite angle, with the load and speed dynamically changing with the direction of oscillation.

[0003] Common failure modes of these bearings include fatigue failure, wear failure, and corrosion failure. Compared with conventional rolling bearings, machine block ball bearings place more stringent requirements on load-carrying capacity, wear resistance, and anti-wear performance. Under small swing angle conditions, where the critical swing angle is used as the criterion, wear failure becomes the main failure mode of machine block oscillating ball bearings. Excessive wear of the bearing raceway will cause a series of problems such as increased frictional torque, reduced load-carrying capacity, and deterioration of motion smoothness, seriously affecting bearing performance and service safety. Currently, due to the lack of a quantitative calculation method for bearing wear applicable to small swing angle conditions, it is difficult to accurately assess bearing wear life and to accurately select swing parameters dominated by wear failure.

[0004] Therefore, based on the motion mechanism and contact characteristics of airframe oscillating ball bearings, establishing a wear life prediction method suitable for small oscillation angle conditions, and optimizing oscillation parameters accordingly, is of great engineering significance for ensuring the operational safety and reliability of large aircraft and helicopters. It also helps to improve the airframe ball bearing life assessment system based on wear amount as the design criterion. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting the wear life of ball bearings at small swing angles and a method for optimizing parameters, which can effectively solve the problems that the wear life of bearings under small swing angle conditions cannot be quantitatively evaluated and that the optimal swing parameters lack theoretical basis.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for predicting the wear life of a ball bearing at a small swing angle, comprising the following steps: S1, Analyze the oscillating motion mechanism of the ball bearing in the machine body, and define the critical oscillation angle of the bearing. And the swing angle of the computer ball bearing under service conditions. Less than the critical swing angle At that time, the number of stress cycles within a single oscillation period ; S2, Based on the swing motion mechanism of the ball bearing, perform motion analysis on the steel ball and calculate the slippage speed of the steel ball relative to the inner raceway and the slippage speed relative to the outer raceway. S3, Establish a calculation model for the contact pressure between the steel ball and the inner and outer grooves, and calculate the contact pressure between the steel ball and the grooves based on the model; S4. Based on the Arcard wear theory, and combined with the slippage speed and contact pressure, a model for calculating the wear depth between the steel ball and the groove is established. S5. Based on the wear depth calculation model, establish a method for predicting the wear life of the machine body ball bearing under small swing angle conditions; S6, execute the wear life prediction method and output the predicted wear life.

[0007] As a preferred embodiment, in step S1, the critical swing angle The calculation formula is: in, The number of steel balls; Let the diameter D of the steel ball be... w With bearing pitch circle diameter d m The ratio; ± indicates that the inner circle is positive and the outer circle is negative.

[0008] As a preferred embodiment, in step S1, when the swing angle Less than the critical swing angle At that time, the number of stress cycles in a single oscillation period =2.

[0009] As a preferred embodiment, in step S2, the slippage speed of the steel ball relative to the inner ring... Compared to the slip speed of the outer ring The calculation formulas are as follows: in, The bearing pitch circle diameter; The angular velocity of the steel ball's revolution; This refers to the angular velocity of the inner ring of the bearing. This refers to the angular velocity of the outer ring of the bearing. Let be the angular velocity of the steel ball's rotation.

[0010] As a preferred embodiment, the contact pressure calculation model in step S3 is as follows: in, The radial load on the ball bearings of the machine body; This represents the maximum normal contact load between the steel ball and the groove; For the radial integral of the load distribution; For load distribution range parameters; For the first The normal contact load between the steel ball and the channel; For the first The maximum contact pressure between the steel ball and the groove. , The major and minor semi-axis of the contact area.

[0011] As a preferred embodiment, in step S4, the wear depth calculation model is as follows: in, For wear depth, The wear coefficient of the material; For contact pressure; Relative sliding speed; The sliding time; It represents the yield strength.

[0012] As a preferred option, the wear depth of the bearing inner ring... and outer ring wear depth Calculated separately as follows: in, Let be a material constant, which is expressed as .

[0013] As a preferred embodiment, the wear life prediction method in step S5 is as follows: in, For wear life; This refers to the radial load on the bearing. This refers to the wear depth. The swing angle; The oscillation frequency; , , , The model index is determined based on Archard's wear theory; when When the wear life is reached, it is determined that the wear life has been reached.

[0014] As a preferred solution, in solving the wear life When considering the radial integral of the load distribution caused by the change in bearing clearance with wear depth, The changes are solved using an iterative method.

[0015] Secondly, the present invention provides a method for optimizing the parameters of a ball bearing under small swing angle operating conditions, comprising the following steps: T1, set the bearing's limit wear index, and use the above-mentioned wear life prediction method to establish the relationship between bearing wear life and oscillation angle and oscillation frequency; T2. Based on the aforementioned relationship, plot the constant wear life curve with the swing angle and swing frequency as the coordinate axes; T3, based on the limit wear index, select the combination of swing angle and swing frequency parameters that meet the target life requirements from the equal wear life curve.

[0016] According to the above technical solution, the beneficial effects of the present invention are: This invention, based on Archard's wear theory, constructs a predictive model that accurately characterizes the quantitative relationship between oscillation angle, oscillation frequency, and wear life. It effectively solves the problem of quantitatively assessing bearing wear under small oscillation angle conditions in existing technologies. By introducing critical oscillation angle criteria, slippage velocity analysis, and contact pressure calculation, the evolution law of small oscillation angle wear is revealed mechanistically, significantly improving the accuracy of life prediction. Simultaneously, the model considers the dynamic impact of wear-induced clearance changes on load distribution and uses an iterative method for solution, making the prediction results more consistent with engineering realities. Furthermore, based on the above model, an intuitive and reliable method for optimizing operating parameters is provided, capable of generating iso-wear life curves, providing designers with a basis for quickly and accurately selecting the optimal combination of oscillation angle and frequency under different life requirements. This invention extends bearing service life from the design stage, significantly improves the reliability and safety of aircraft control systems, and supplements and improves the airframe ball bearing life design system with wear as a control indicator. Attached Figure Description

[0017] Figure 1 This diagram illustrates the effect of the critical swing angle on the stress volume distribution when the swing angle of the ball bearing in the machine body is less than the critical swing angle. Figure 2 This diagram illustrates the effect of the critical swing angle on the stress volume distribution when the swing angle of the ball bearing in the machine body is greater than the critical swing angle. Figure 3 A schematic diagram of the iterative solution process for wear life; Figure 4 The graph shows the relationship between wear life and oscillation angle and oscillation frequency.

[0018] The markings in the diagram are: 1. Bearing outer ring, 2. Bearing inner ring, 3. Steel ball, 4. Stress volume, 5. Overlapping area of ​​stress volume. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0020] The structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0021] like Figure 1 and Figure 2 As shown, Figure 1 The diagram illustrates the ideal effect of the critical swing angle on the stress volume distribution when the swing angle of the ball bearing is less than the critical swing angle. Under this condition, the stress volume 4 formed by the contact between the steel ball 3 and the inner ring 2 groove and the outer ring 1 groove is independent of each other and does not overlap. This is the typical contact state of small swing angle wear that this invention addresses. Figure 2 The diagram shows a comparison of stress volume distribution when the swing angle is greater than the critical swing angle. At this time, there is an overlap region 5 of stress volume between the stress volumes 4 corresponding to the motion trajectories of adjacent steel balls. This overlap effect will significantly change the stress cycle characteristics of the contact area, thus making the wear model based on the small swing angle assumption no longer applicable.

[0022] In this embodiment, the specific structural parameters, material parameters, and operating parameters of the ball bearing are as follows: pitch circle diameter mm, steel ball diameter mm, number of steel balls inner groove curvature radius mm, outer groove radius of curvature mm, bearing material is GCr15, bearing operating conditions are radial load of 30kN.

[0023] In this embodiment, the swing angle of the ball bearing under service conditions is... The angle is 8.3°, and the allowable wear depth is 0.004 mm.

[0024] This embodiment of a method for predicting the wear life of a ball bearing at a small swing angle is implemented through an iterative process, as follows: Figure 3 As shown, it includes the following steps: S1, Analyze the oscillating motion mechanism of the ball bearing in the machine body, and define the critical oscillation angle of the bearing. Critical swing angle The calculation formula is: (1) in, The number of steel balls; Let the diameter D of the steel ball be... w With bearing pitch circle diameter d m The ratio; ± indicates that the inner ring is positive and the outer ring is negative. And the swing angle of the computer-controlled ball bearing under service conditions. Less than the critical swing angle At that time, the number of stress cycles within a single oscillation period ; In this embodiment, all initial parameters are input, including the number of steel balls. steel ball diameter mm, pitch circle diameter mm, substituting into formula (1), we obtain that the critical swing angle of the inner circle is approximately 19.9° and the critical swing angle of the outer circle is approximately 30.3°. Taking the smaller value as the unified criterion, therefore, =19.9°.

[0025] Determine the currently set swing angle Is it less than the critical swing angle? If this condition is not met, the process terminates and the model is not applicable; if it is met, the bearing is in the "small swing angle" working state targeted by this invention, the model is applicable, and the core calculation loop is entered. Specifically, in this embodiment, the swing angle of the ball bearing's service condition is set. It is 8.3°, which is less than the critical swing angle. Therefore, under these conditions, the number of stress cycles in a single oscillation period is: (2) S2, Based on the oscillating motion mechanism of the ball bearing, perform motion analysis on the steel ball and calculate the slippage speed of the steel ball relative to the inner raceway. Compared to the slip speed of the outer groove The slippage speed of the steel ball relative to the inner circle Compared to the slip speed of the outer ring The calculation formulas are as follows: (3) (4) in, The bearing pitch circle diameter; The angular velocity of the steel ball's revolution; This refers to the angular velocity of the inner ring of the bearing. This refers to the angular velocity of the outer ring of the bearing. Let be the angular velocity of the steel ball's rotation.

[0026] Calculate the slippage speed of the steel ball relative to the inner ring using formulas (3) and (4). and the slip speed relative to the outer edge .

[0027] S3. Establish a calculation model for the contact pressure between the steel ball and the inner and outer grooves. Based on this model, calculate the contact pressure between the steel ball and the grooves. The contact pressure calculation model is as follows: (5) in, The radial load on the ball bearings of the machine body; This represents the maximum normal contact load between the steel ball and the groove; For the radial integral of the load distribution; For load distribution range parameters; For the first The normal contact load between the steel ball and the channel; For the first The maximum contact pressure between the steel ball and the groove. , The major and minor semi-axis of the contact area.

[0028] In this embodiment, based on the radial load F = 30kN on the bearing, and combined with formula (5), the maximum contact pressure between the steel ball and the inner and outer raceways is calculated. (Unit: GPa).

[0029] S4, based on Arcard wear theory, combined with the slippage speed and and contact pressure A calculation model for the wear depth between the steel ball and the groove is established; the wear depth calculation model is as follows: (6) in, For wear depth, The wear coefficient of the material; For contact pressure; Relative sliding speed; The sliding time; It represents the yield strength.

[0030] Bearing inner ring wear depth and outer ring wear depth Calculated separately as follows: (7) (8) in, Here is a material constant, expressed as: (9) In this embodiment, the slippage speed calculated in steps S2 and S3 is used as the basis for the calculation. , and contact pressure Substituting into formulas (7) and (8), and performing calculations respectively, the increase in inner ring wear depth within one oscillation cycle can be obtained. and outer ring wear depth increment .

[0031] S5. Based on the wear depth calculation model, a wear life prediction method for the ball bearing of the machine body under small swing angle conditions is established. The wear life prediction method is as follows: (10) in, For wear life; This refers to the radial load on the bearing. This refers to the wear depth. The swing angle; The oscillation frequency; , , , The model index is determined based on Archard's wear theory; when When the wear life is reached, it is determined that the wear life has been reached.

[0032] Determine whether the total wear depth has reached the service life threshold. Specifically, when the sum of the cumulative wear depths of the inner and outer rings reaches the allowable wear depth, i.e., the cumulative wear depth... achieve When the wear life is reached, it is determined. In solving for the wear life... When considering the radial integral of the load distribution caused by the change in bearing clearance with wear depth, The changes are solved using an iterative method.

[0033] In this embodiment, the allowable wear depth is 0.004 mm. An iterative method is used for lifetime prediction. The iteration begins by calculating the wear depth increment obtained in step S4. and Add them together to get the wear depth And determine the depth of wear. Has the allowable wear depth of 0.004 mm been reached? If the wear depth... If the value is ≥0.004mm, the iteration ends immediately, and the current cumulative number of oscillation cycles is recorded. This is the predicted wear life. If it is not reached, proceed to the next step to continue the iteration.

[0034] As wear leads to material loss, the internal clearance of the bearing changes. In this step, the bearing's geometry and clearance are updated to reflect the latest wear condition. After the update is complete, the process returns to the beginning of step S2, and the wear analysis for the next oscillation cycle is performed again based on the new bearing geometry.

[0035] Through iterative cycles of steps S2 to S5, the precise wear life at a specific operating point (8.3°, 0.7Hz) can be calculated. It is 11,000 times.

[0036] In this embodiment, a method for optimizing parameters of a ball bearing operating at a small swing angle is provided, based on the above prediction method, to optimize the parameters: T1 sets the bearing's limit wear index. In this embodiment, the limit wear index is defined as the allowable wear depth of the raceway. =0.004mm; Using the above wear life prediction method, within the predetermined swing angle and swing frequency parameter range, the swing angle is established by systematically repeating the iterative calculations of steps S1 to S5. oscillation frequency The number of oscillations corresponding to reaching this limit of wear (i.e., wear life) The relationship between ). Specifically, given a target lifetime. =11000 times. By calculation, the set of all operating points that can make the predicted life equal to 11000 times can be obtained, thus forming an equal wear life curve on the graph.

[0037] T2, based on the relationship established in step T1, plots an isowear life curve with oscillation angle and oscillation frequency as coordinate axes; in this embodiment, by giving a series of different target lives (such as 8000, 9000, 10000, and 12000 oscillations), the above calculation process is repeated, and finally a chart containing multiple isowear life curves is plotted, such as... Figure 4 As shown in the figure. Each curve in the figure represents a specific target lifetime, and the coordinates of any point on the curve are (…). , All of them meet the same lifespan requirements.

[0038] T3: Based on the aforementioned limit wear index, select a combination of oscillation angle and oscillation frequency parameters from the equal wear life curve to meet the target life requirement. In this embodiment, a lifespan of not less than 11,000 cycles is required, therefore... Figure 4 Select point G (8.3°, 0.7Hz) on the curve of 11,000 times.

[0039] Based on the specific design requirements for lifespan, the combination of oscillation angle and oscillation frequency parameters that meets the target lifespan requirement is selected from the wear life curve plotted in step T2. In this embodiment, if the design requires a wear lifespan... If the number of oscillations is not less than 11,000, then the designers can directly... Figure 4 Select a suitable operating point on the curve corresponding to 11,000 cycles, for example: point G (8.3°, 0.7Hz). To improve design reliability and increase safety margin, parameters can be selected within the range below this curve, such as combinations of (7.5°, 0.7Hz) or (8.3°, 0.6Hz), which can ensure that the actual lifespan is better than the design specifications.

[0040] It should be noted that the above embodiments are only used to illustrate the present invention, but the present invention is not limited to the above embodiments. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the wear life of a ball bearing at a small swing angle, characterized in that, Includes the following steps: S1, Analyze the oscillating motion mechanism of the ball bearing in the machine body, and define the critical oscillation angle of the bearing. And the swing angle of the computer ball bearing under service conditions. Less than the critical swing angle At that time, the number of stress cycles within a single oscillation period ; S2, Based on the swing motion mechanism of the ball bearing, perform motion analysis on the steel ball and calculate the slippage speed of the steel ball relative to the inner raceway and the slippage speed relative to the outer raceway. S3, Establish a calculation model for the contact pressure between the steel ball and the inner and outer grooves, and calculate the contact pressure between the steel ball and the grooves based on the model; S4. Based on the Arcard wear theory, and combined with the slippage speed and contact pressure, a model for calculating the wear depth between the steel ball and the groove is established. S5. Based on the wear depth calculation model, establish a method for predicting the wear life of the machine body ball bearing under small swing angle conditions; S6, execute the wear life prediction method and output the predicted wear life.

2. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 1, characterized in that: In step S1, the critical swing angle The calculation formula is: in, The number of steel balls; Let the diameter D of the steel ball be... w With bearing pitch circle diameter d m The ratio; ± indicates that the inner circle is positive and the outer circle is negative.

3. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 2, characterized in that: In step S1, when the swing angle Less than the critical swing angle At that time, the number of stress cycles in a single oscillation period =2.

4. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 1, characterized in that: In step S2, the slippage speed of the steel ball relative to the inner ring and the slip speed relative to the outer edge The calculation formulas are as follows: in, The bearing pitch circle diameter; The angular velocity of the steel ball's revolution; This refers to the angular velocity of the inner ring of the bearing. This refers to the angular velocity of the outer ring of the bearing. Let be the angular velocity of the steel ball's rotation.

5. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 1, characterized in that: In step S3, the contact pressure calculation model is as follows: in, The radial load on the ball bearings of the machine body; This represents the maximum normal contact load between the steel ball and the groove; For the radial integral of the load distribution; For load distribution range parameters; For the first The normal contact load between the steel ball and the channel; For the first The maximum contact pressure between the steel ball and the groove. , The major and minor semi-axis of the contact area.

6. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 1, characterized in that: In step S4, the wear depth calculation model is as follows: in, For wear depth, The wear coefficient of the material; For contact pressure; Relative sliding speed; The sliding time; It represents the yield strength.

7. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 6, characterized in that: Bearing inner ring wear depth and outer ring wear depth Calculated separately as follows: in, Let be a material constant, which is expressed as .

8. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 1, characterized in that: In step S5, the wear life prediction method is as follows: in, For wear life; This refers to the radial load on the bearing. This refers to the wear depth. The swing angle; The oscillation frequency; , , , The model index is determined based on Archard's wear theory; when When the wear life is reached, it is determined that the wear life has been reached.

9. The method for predicting the wear life of a ball bearing with a small swing angle according to claim 8, characterized in that: In solving wear life When considering the radial integral of the load distribution caused by the change in bearing clearance with wear depth, The changes are solved using an iterative method.

10. A method for optimizing the parameters of a ball bearing operating at a small swing angle, characterized in that: Includes the following steps: T1, set the bearing's limit wear index, and use the wear life prediction method according to any one of claims 1-8 to establish the relationship between bearing wear life and oscillation angle and oscillation frequency; T2. Based on the aforementioned relationship, plot the constant wear life curve with the swing angle and swing frequency as the coordinate axes; T3, based on the limit wear index, select the combination of swing angle and swing frequency parameters that meet the target life requirements from the equal wear life curve.

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