Dynamic modeling method, device and equipment for slewing bearing of ultra-large-diameter antenna and medium

Abstract

The invention discloses a dynamical modeling method, device and equipment for a slewing bearing of an ultra-large-diameter antenna and a medium, and relates to the technical field of ultra-large-diameter antennae, and the method comprises the steps: obtaining the structural parameters of the slewing bearing; according to the structural parameters of the slewing bearing, calculating the contact stress at the t-th moment and the contact area at the t-th moment; according to the contact stress at the t-th moment and the contact area at the t-th moment, the interaction force between the rolling ball and the raceway at the t-th moment and the acting torque at the t-th moment are obtained; establishing a dynamic modeling equation, and calculating the acceleration of the slewing bearing at the t-th moment according to the dynamic modeling equation; and judging whether the t-th moment reaches a set time length, and if the t-th moment reaches the set time length, completing modeling calculation. According to the method, the calculation cost can be reduced, the dependence on software and a network is reduced, and the flexibility is higher.

Description

Technical Field

[0001] The present application relates to the technical field of ultra-large-aperture antennas, and particularly to a dynamic modeling method, device, equipment and medium for a slewing bearing of an ultra-large-aperture antenna. Background Art

[0002] As the core component for attitude adjustment of an ultra-large-aperture reflector antenna, the dynamic characteristics of the slewing bearing directly affect the pointing accuracy of the antenna beam. Conducting dynamic modeling on it not only helps optimize the design, predict faults, improve efficiency, but also provides theoretical support for the research and development of new products. Through dynamic modeling, the behavior of the bearing can be better understood and controlled, thereby improving the reliability and performance of the system.

[0003] However, due to the special structure and motion form of the slewing bearing, the commonly used lumped parameter modeling method for bearings only analyzes each part of the bearing in a plane and is not applicable to the slewing bearing. And the current dynamic research on four-point angular contact slewing bearings is based on finite element simulation software. This research method has a high calculation cost and a high dependence on software and meshes. Summary of the Invention

[0004] The present application provides a dynamic modeling method, device, equipment and medium for a slewing bearing of an ultra-large-aperture antenna, which can reduce the calculation cost, reduce the dependence on software and network, and have higher flexibility.

[0005] To achieve the above object, the present application adopts the following technical solutions: In a first aspect, the present application provides a dynamic modeling method for a slewing bearing of an ultra-large-aperture antenna, the method comprising: Obtain the structural parameters of the slewing bearing in the antenna; According to the structural parameters of the slewing bearing, calculate the contact stress at the t-th moment and the contact area at the t-th moment; According to the contact stress at the t-th moment and the contact area at the t-th moment, calculate the lubrication traction force at the t-th moment between the rolling balls and the inner and outer raceways; According to the contact stress at the t-th moment and the lubrication traction force at the t-th moment, obtain the interaction force at the t-th moment and the moment of force at the t-th moment between the rolling balls and the raceways; According to the interaction force at the t-th moment and the moment of force at the t-th moment between the rolling balls and the raceways, establish a dynamic modeling equation, and according to the dynamic modeling equation, calculate the acceleration of the slewing bearing at the t-th moment; Judge whether the t-th moment reaches a set duration, obtain a first judgment result, if the first judgment result indicates that the t-th moment reaches the set duration, then output the acceleration of the slewing bearing at the t-th moment and at each moment before the t-th moment.

[0006] In some possible implementations, the method further includes: If the first judgment result indicates that the set duration has not been reached at the t-th moment, calculate the acceleration of the slewing bearing at the (t + 1)-th moment.

[0007] In some possible implementations, the calculating the contact stress at the t-th moment includes: Obtain the contact deformation amount between the rolling ball and the lower half of the inner raceway, and calculate the contact stress at the t-th moment according to the contact deformation amount between the rolling ball and the lower half of the inner raceway; The obtaining the contact deformation amount between the rolling ball and the lower half of the inner raceway includes: Judge the first value Whether it is greater than zero and whether the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring is less than zero, to obtain the first judgment result. If the first judgment result indicates that the first value is greater than zero and the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring is less than zero, then determine the first value as the contact deformation amount between the rolling ball and the lower half of the inner raceway; Make the judgment through the following formula:

[0008]

[0009]

[0010] wherein, is the contact deformation amount between the rolling ball and the lower half of the inner raceway, is the position of the center of curvature of the raceway relative to the center of the ball of the rolling ball in the contact coordinate system, is the groove curvature coefficient of the lower half of the inner raceway, is the diameter of the rolling ball, is the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring, is the position of the center of the ball of the rolling ball in the fixed body coordinate system of the inner ring, is the position of the center of curvature of the raceway in the fixed body coordinate system of the inner ring, is the x coordinate value of the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring; According to the contact deformation amount between the rolling ball and the lower half of the inner raceway and the Hertz contact theory, the contact stress at the t-th moment can be calculated.

[0011] In some possible implementations, the calculating the lubrication traction force between the rolling ball and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the contact area at the t-th moment includes: Calculate the relative velocity of the raceway relative to the rolling ball at point p according to the contact area at the t-th moment, and then calculate the traction coefficient according to the relative velocity of the raceway relative to the rolling ball at point p. Calculate the lubrication traction force between the rolling ball and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the traction coefficient.

[0012] In some possible implementation manners, obtaining the interaction force and the moment of force at the t-th moment between the rolling ball and the raceway according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment includes:

[0013] Among them, is the force exerted on the rolling ball by the raceway in the contact coordinate system of the rolling element and the inner and outer rings, is the lubrication traction force at the t-th moment, is the contact stress at the t-th moment; Among them, the moment of force at the t-th moment includes the moment of the rolling ball on the inner raceway and the moment of the raceway on the rolling ball. The moment of the rolling ball on the inner raceway is calculated by the following formula:

[0014] The moment of the raceway on the rolling ball is calculated by the following formula:

[0015] Among them, is the moment of the rolling ball on the inner raceway, is the position of the contact area of the rolling ball relative to the center of the ball in the rolling element orientation coordinate system, is the force exerted on the rolling ball by the raceway in the rolling element orientation coordinate system, is the moment of the raceway on the rolling ball, is the position of the contact point p on the raceway relative to the center of the inner ring in the fixed coordinate system of the inner ring, is the force exerted on the raceway by the rolling ball in the fixed coordinate system of the inner ring.

[0016] In some possible implementation manners, the method further includes: The contact area at the t-th moment is elliptical. Calculate the major semi-axis of the contact area at the t-th moment according to the contact stress at the t-th moment. The major semi-axis of the contact area at the t-th moment is used to calculate the lubrication traction force at the t-th moment; Calculating the major semi-axis of the contact area at the t-th moment includes:

[0017] Among them, is the major semi-axis of the contact area at the t-th moment, k is the ellipticity of the contact area, The second kind of complete elliptic integral of the k where is the equivalent curvature radius, is the contact stress at the t-th moment, is the equivalent elastic modulus.

[0018] In some possible implementation manners, the method further includes: Processing the acceleration of the slewing bearing at the t-th moment by using the fourth-order Runge-Kutta method to obtain the speed and displacement of the slewing bearing at the t-th moment, and predicting the service life of the slewing bearing according to the speed and displacement.

[0019] In a second aspect, the present application provides a dynamics modeling device for a slewing bearing of an extra-large aperture antenna, and the device includes: An acquisition module, configured to acquire the structural parameters of the slewing bearing in the antenna; A calculation module, configured to calculate the contact stress at the t-th moment and the contact area at the t-th moment according to the structural parameters of the slewing bearing; calculate the lubrication traction force at the t-th moment between the rolling balls and the inner and outer raceways according to the contact stress at the t-th moment and the contact area at the t-th moment; obtain the interaction force at the t-th moment and the acting moment at the t-th moment between the rolling balls and the raceways according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment; establish a dynamics modeling equation according to the interaction force at the t-th moment and the acting moment at the t-th moment between the rolling balls and the raceways, and calculate the acceleration of the slewing bearing at the t-th moment according to the dynamics modeling equation; A judgment module, configured to judge whether the t-th moment reaches a set duration to obtain a first judgment result, and if the first judgment result indicates that the t-th moment reaches the set duration, output the acceleration of the slewing bearing at the t-th moment and each moment before the t-th moment.

[0020] In a third aspect, the present application provides a computing device, including a memory and a processor; wherein, one or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device is enabled to execute the method according to any one of the first aspect.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium, and the computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method according to any one of the first aspect.

[0022] In a fifth aspect, the present application provides a computer program product, and the computer program product includes one or more computer instructions, and when the computer instructions are executed by a computer, the computer executes the method according to any one of the first aspect.

[0023] As can be seen from the above technical solutions, the present application has at least the following beneficial effects: In the present application, structural parameters of the slewing bearing in the antenna are obtained; an interaction model between the slewing bearing and the inner and outer rings is constructed, and according to the structural parameters of the slewing bearing, the contact stress at the t-th moment and the contact area at the t-th moment are calculated; according to the contact stress at the t-th moment and the contact area at the t-th moment, the lubrication traction force between the rolling balls and the inner and outer raceways at the t-th moment is calculated; then according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment, the interaction force and the moment of force at the t-th moment between the rolling balls and the raceways are obtained; furthermore, according to the interaction force and the moment of force at the t-th moment between the rolling balls and the raceways, a dynamic modeling equation is established, and according to the dynamic modeling equation, the acceleration of the slewing bearing at the t-th moment is calculated; it is judged whether the t-th moment reaches a set duration to obtain a first judgment result, and if the first judgment result indicates that the t-th moment reaches the set duration, the modeling calculation is completed. Currently, the dynamic research on four-point angular contact slewing bearings is carried out based on finite element simulation software. This research method has a high calculation cost and a high dependence on software and meshes. Therefore, the present application provides a dynamic modeling method for the slewing bearing of an ultra-large-aperture antenna. By combining theoretical derivation and numerical calculation, the calculation cost can be effectively reduced, and there is no need for expensive computing equipment and a large amount of computing time. This method can be realized based on general mathematical calculation tools and programming languages, is not limited to specific finite element software, and improves the flexibility of the research. Moreover, this method has a very low dependence on meshes, avoiding errors and complexities brought by mesh division problems, and making the research process more efficient.

[0024] It should be understood that the description of technical features, technical solutions, beneficial effects or similar languages in the present application does not imply that all features and advantages can be achieved in any single embodiment. On the contrary, it can be understood that the description of features or beneficial effects means that specific technical features, technical solutions or beneficial effects are included in at least one embodiment. Therefore, the description of technical features, technical solutions or beneficial effects in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in this embodiment can be combined in any appropriate manner. Those skilled in the art will understand that an embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flowchart of a dynamic modeling method for the slewing bearing of an ultra-large-aperture antenna provided by an embodiment of the present application; Figure 2 Schematic diagram of a coordinate system defined on a slewing bearing provided by an embodiment of the present application; Figure 3 Schematic diagram of a dynamics modeling device for a slewing bearing of an ultra-large aperture antenna provided by an embodiment of the present application; Figure 4 Schematic diagram of a computing device provided by an embodiment of the present application. Detailed implementation manners

[0026] Terms such as "first", "second", and "third" in the specification and drawings of the present application are used to distinguish different objects, rather than to limit a specific order.

[0027] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific manner.

[0028] For the sake of clear and concise description of the following embodiments, a brief introduction to the related art is given first: The four-point angular contact slewing bearing consists of components such as an inner ring, an outer ring, rolling elements (usually balls), and a cage. Its structural feature is that the contact points between the balls and the raceways can form four load-bearing contact angles, which gives it unique advantages in bearing combined loads such as axial force, radial force, and overturning moment. When the equipment is running, if there are acting forces in multiple directions, the four-point angular contact slewing bearing can evenly distribute the loads through these four contact points, effectively improving the load-bearing capacity.

[0029] In practical applications, four-point angular contact slewing bearings are commonly found in equipment with high requirements for slewing accuracy and load-bearing capacity. For example, in the joint parts of industrial robots, it can ensure the precise positioning of the robotic arm during complex movements and at the same time bear multi-directional forces generated by grasping heavy objects, etc.; in the slewing mechanism of an aerial work platform, it can bear the self-weight of the platform and various loads during operation, ensuring the stable rotation of the platform and providing safe and reliable working conditions for the operators.

[0030] Currently, the lumped parameter modeling method for bearings only analyzes each part of the bearing in a plane and is not applicable to slewing bearings. The current dynamic research on four-point angular contact slewing bearings is only based on finite element simulation software. This research method has a high calculation cost and a high dependence on software and meshes.

[0031] In view of this, an embodiment of the present application provides a dynamic modeling method for the slewing bearing of an ultra-large aperture antenna. In this method, the structural parameters of the slewing bearing are obtained; an interaction model between the slewing bearing and the inner and outer rings is constructed, and according to the structural parameters of the slewing bearing, the contact stress at the t-th moment and the contact area at the t-th moment are calculated; according to the contact stress at the t-th moment and the contact area at the t-th moment, the lubrication traction force between the rolling balls and the inner and outer raceways at the t-th moment is calculated; then, according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment, the interaction force and the acting moment at the t-th moment between the rolling balls and the raceways are obtained; furthermore, according to the interaction force and the acting moment at the t-th moment between the rolling balls and the raceways, a dynamic modeling equation is established, and according to the dynamic modeling equation, the acceleration of the slewing bearing at the t-th moment is calculated; it is judged whether the t-th moment reaches a set duration to obtain a first judgment result. If the first judgment result indicates that the t-th moment reaches the set duration, the modeling calculation is completed. It can be seen that the present application provides a dynamic modeling method for the slewing bearing of an ultra-large aperture antenna. By combining theoretical derivation and numerical calculation, the calculation cost can be effectively reduced, and expensive computing equipment and a large amount of computing time are not required. This method can be implemented based on general mathematical calculation tools and programming languages, is not limited to specific finite element software, and improves the flexibility of research. Moreover, this method has a very low dependence on meshes, avoiding errors and complexities caused by mesh division problems, and making the research process more efficient.

[0032] In order to make the technical solution of the present application clearer and easier to understand, the following will introduce a dynamic modeling method for the slewing bearing of an ultra-large aperture antenna provided by an embodiment of the present application with reference to the accompanying drawings. As Figure 1 shown, this figure is a flowchart of a dynamic modeling method for the slewing bearing of an ultra-large aperture antenna provided by an embodiment of the present application. The dynamic modeling method for the slewing bearing of the ultra-large aperture antenna includes: S101. Obtain the structural parameters of the slewing bearing in the antenna.

[0033] In an embodiment of the present application, taking the slewing bearing of an ultra-large aperture antenna as the background, the parameters of the slewing bearing of the ultra-large aperture antenna are obtained. Among them, the ultra-large aperture antenna is a device for receiving and transmitting electromagnetic wave signals, and its characteristic is that the antenna aperture size is very large. Generally speaking, when the aperture size reaches several meters, dozens of meters or even larger, it can be regarded as an ultra-large aperture antenna.

[0034] Obtain the positions of the centers of the rolling balls in the slewing bearing in each coordinate system. To make the dynamic modeling calculation clearer, each coordinate system is defined, such as Figure 2As shown in the figure, this figure is a schematic diagram of a coordinate system defined on a slewing bearing provided by an embodiment of the present application. It can be seen from the figure that the rectangular inertial coordinate system (X, Y, Z) of the slewing bearing is used as the reference coordinate system, which is the basis for establishing other coordinate systems and the entire slewing bearing model, and is used to describe the translational motion of the rolling balls and the inner ring. Taking the stationary outer ring as the reference, with the center of the curvature trajectory circle of the outer raceway as the origin O, and the central axis of the outer ring as the X-axis, the directions of the Y-axis and Z-axis are determined according to the right-hand rule, where the Z-axis points to the center of the first ball. In order to measure the rotation of the rolling balls and the inner ring, it is necessary to establish an inertial cylindrical coordinate system (x, r, θ). Similar to the inertial rectangular coordinate system, the origin of the cylindrical coordinate system and the X-axis coincide with the inertial rectangular coordinate system. The polar radius r extends outward along the bearing radius, and the polar angle θ is the angle between the polar radius r and the Z-axis of the inertial rectangular coordinate system, with counterclockwise being positive.

[0035] The origin of the inner ring fixed-body coordinate system (Xr, Yr, Zr) is fixed at the center of the inner ring and moves with the movement of the inner ring; the rolling element orientation coordinate system (Xb, Yb, Zb) is synchronized with the revolution of the balls and is used to describe the rotation of the rolling balls. The origin of the rolling element orientation coordinate system is fixed at the centroid of the rolling ball. The Xb-axis in the rolling element orientation coordinate system is parallel and in the same direction as the X-axis of the bearing inertial system. The Zb-axis extends outward along the bearing radius and rotates with the revolution of the rolling balls, without changing with the rotation of the rolling balls. The Yb-axis is determined by the right-hand rule. The rotation speed of the rolling balls is measured in the rolling element orientation coordinate system, and the translational and revolution speeds of the rolling balls are measured in the bearing inertial system.

[0036] Considering that many auxiliary coordinate systems are needed in the model calculation process, such as calculating the forces between each rolling ball and the inner and outer raceways, between the steel balls and the cage, and between the cage and the raceway, it is necessary to determine the position of the contact area and establish a local contact coordinate system to describe the magnitude and direction of the forces. The local coordinate system is defined during the specific calculation.

[0037] S102. Calculate the contact stress at the t-th moment and the contact area at the t-th moment according to the structural parameters of the slewing bearing.

[0038] Construct an interaction model between the slewing bearing and the inner and outer rings to calculate the contact stress generated by mutual contact at the t-th moment. Since both the inner and outer rings of the slewing bearing have a double-half inner ring structure, first determine the relative position between the center of the rolling ball and the center of curvature of the raceway, and then judge whether the rolling ball contacts the upper half or the lower half of the inner raceway. If the rolling ball contacts the lower half of the inner raceway, calculate the contact deformation amount between the rolling ball and the lower half of the inner raceway, and then calculate the contact stress at the t-th moment and the contact area at the t-th moment according to the Hertz contact theory. The following is a detailed introduction to the calculation process. Among them, the expression method of positions in this application is all matrix, such as , is The position of the x-axis in the inertial coordinate system, is The position of the y-axis in the inertial coordinate system, is The position of the z-axis in the inertial coordinate system. The expression of this position is also applicable to the following steps and will not be explained later.

[0039] Convert the position of the center of the rolling ball from the inertial coordinate system to the inner ring fixed body coordinate system: , is the position of the center of the rolling ball in the inertial coordinate system, is the transformation matrix from the inertial coordinate system to the inner ring fixed body coordinate system, is the position of the center of the rolling ball in the inner ring fixed body coordinate system; the corresponding azimuth angle of the rolling ball is: , is the corresponding azimuth angle of the rolling ball, is the y coordinate value of the center of the rolling ball in the inertial coordinate system, is the z coordinate value of the center of the rolling ball in the inertial coordinate system; thus, the coordinates of the curvature center of the raceway in the inner ring fixed body coordinate system are obtained: , is the x-axis coordinate value of the curvature center of the raceway in the inner ring fixed body coordinate system, is the polar radius of the curvature center of the raceway in the inner ring fixed body coordinate system, where and are determined by the structural parameters of the raceway itself.

[0040] In the inner ring fixed body coordinate system, calculate the position of the curvature center of the raceway relative to the center of the rolling ball: , and then convert the position of the curvature center of the raceway relative to the center of the rolling ball from the inner ring fixed body coordinate system to the rolling element azimuth coordinate system. The transformation matrix from the inner ring fixed body coordinate system to the rolling element azimuth coordinate system is , means that the parameter position first rotates degrees around the x-axis, then rotates 0 degrees around the y-axis of the rotated coordinate system, and finally rotates 0 degrees around the z-axis of this coordinate system. Therefore, the position of the curvature center of the raceway relative to the center of the rolling ball in the rolling element azimuth coordinate system is , and then calculate the contact angle between the rolling ball and the raceway: , is the contact angle between the rolling ball and the raceway, is the x coordinate value of the curvature center of the raceway relative to the center of the rolling ball in the rolling element azimuth coordinate system, The z - coordinate value of the curvature center of the raceway relative to the center of the ball in the rolling - element azimuth coordinate system, and then the position of the curvature center of the raceway relative to the center of the ball is transformed from the rolling - element coordinate system to the rolling - element and inner - outer - ring contact coordinate system. The transformation matrix for transforming the rolling - element coordinate system to the rolling - element and inner - outer - ring contact coordinate system is , so the position of the curvature center of the raceway relative to the center of the ball in the rolling - element and inner - outer - ring contact coordinate system is .

[0041] Since the ball is in circular motion, studying the forces in each azimuth system and calculating the position coordinates in different coordinate systems can facilitate the representation of forces in the subsequent equilibrium equations.

[0042] From the above, the contact deformation amount between the ball and the lower half - circle of the inner raceway can be obtained according to the position of the curvature center of the raceway relative to the center of the ball in the rolling - element and inner - outer - ring contact coordinate system, and the contact stress at the t - th moment can be calculated based on the contact deformation amount between the ball and the lower half - circle of the inner raceway.

[0043] Among them, obtaining the contact deformation amount between the ball and the lower half - circle of the inner raceway requires first judging the first value whether it is greater than zero and whether the position vector of the contact point relative to the coordinate origin in the inner - ring fixed - body coordinate system is less than zero, to obtain the first judgment result. If the first judgment result indicates that the first value is greater than zero and the position vector of the contact point relative to the coordinate origin in the inner - ring fixed - body coordinate system is less than zero, then determine the first value as the contact deformation amount between the ball and the lower half - circle of the inner raceway; the judgment is carried out through the following formula:

[0044]

[0045]

[0046] Among them, is the contact deformation amount between the ball and the lower half - circle of the inner raceway, is the position of the curvature center of the raceway relative to the center of the ball in the contact coordinate system, is the groove curvature coefficient of the lower half - raceway of the inner ring, is the ball diameter, is the position vector of the contact point relative to the coordinate origin in the inner - ring fixed - body coordinate system, is the position of the center of the ball in the inner - ring fixed - body coordinate system, is the position of the curvature center of the raceway in the inner - ring fixed - body coordinate system, is the x - coordinate value of the position vector of the contact point relative to the coordinate origin in the inner - ring fixed - body coordinate system.

[0047] Then, based on the contact deformation of the rolling ball with the lower half of the inner raceway and Hertz contact theory, the contact stress at the t-th moment can be calculated, and the calculation formula is as follows:

[0048]

[0049] Where, is the contact stress at the t-th moment, is the elastic modulus, k is the ellipticity of the contact area, is k the first complete elliptic integral of the first kind of is k the second complete elliptic integral of the second kind of is the equivalent curvature radius, is the equivalent elastic modulus.

[0050] The ellipticity k of the contact area needs to be obtained by numerical iteration, and the initial value has an approximate formula:

[0051] The ellipticity k at the (n + 1)-th iteration is obtained by the following formula:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Where, is the ellipticity of the contact area, is the curvature radius in the x direction, is the curvature radius in the y direction, is the total equivalent curvature radius, is k the first complete elliptic integral of the first kind of is k the second complete elliptic integral of the second kind of is the curvature radius of the inner raceway in the x direction, is the radius of curvature of the inner raceway in the y direction, is the curvature of the inner raceway in the x direction, is the curvature of the inner raceway in the y direction, is the curvature of the rolling ball in the x direction, is the curvature of the rolling ball in the y direction, is the diameter of the rolling ball, is an intermediate process formula.

[0060] S103. Calculate the lubrication traction force between the rolling ball and the inner and outer raceways according to the contact stress and the contact area at the t-th moment.

[0061] Calculate the relative velocity of the raceway with respect to the rolling ball at point p according to the contact area at the t-th moment, then calculate the traction coefficient according to the relative velocity of the raceway with respect to the rolling ball at point p, and calculate the lubrication traction force between the rolling ball and the inner and outer raceways at the t-th moment according to the contact stress and the traction coefficient at the t-th moment. The following is a detailed introduction to the calculation process.

[0062] Under the condition of the slewing bearing running, at the t-th moment, calculate the radius of curvature of the deformed compressed surface: , is the groove curvature coefficient of the inner ring, which is a structural parameter. Therefore, the position of the contact area of the rolling ball relative to the center of the ball in the contact coordinate system of the rolling element and the inner and outer rings can be expressed as , is the semi-major axis of the contact area at the t-th moment. In order to obtain the traction coefficient, it is necessary to obtain the relative velocity of the raceway with respect to the rolling ball at point p. In order to obtain the relative velocity of the raceway with respect to the rolling ball at point p, it is also necessary to calculate the velocity of the contact point p of the rolling ball, the position of the contact area of the rolling ball relative to the center of the ball in the inertial coordinate system, and the position of the contact area of the raceway relative to the center of the rolling ring. The calculation formulas are as follows:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] Among them, is the velocity of the contact point p of the rolling ball, is the transformation matrix for converting the rolling element coordinate system to the contact coordinate system of the rolling element and the inner and outer rings, is the axial velocity of the rolling ball, is the velocity in the radial direction of the rolling ball, is the transformation matrix from the inertial coordinate system to the azimuth coordinate system, is the rotational velocity of the rolling ball at the previous moment, is the position of the curvature center of the raceway relative to the center of the ball of the rolling ball in the contact coordinate system of the rolling element and the inner and outer rings, is the position of the contact area of the rolling ball relative to the center of the ball in the inertial coordinate system, is the position of the contact area of the raceway relative to the center of the rolling ring, is the position of the center of the ball of the rolling ball in the fixed coordinate system of the inner ring, is the velocity of the contact point p of the raceway, The translational velocity of the inner ring at the previous moment, is the rotational velocity of the inner ring at the previous moment, is the relative velocity of the raceway relative to the rolling ball at point p, is the traction coefficient, 、 、 and are the first coefficient, the second coefficient, the third coefficient and the fourth coefficient respectively.

[0069] The contact area at the t-th moment is elliptical in shape. The major semi-axis and minor semi-axis of the contact area at the t-th moment can also be calculated according to the contact stress at the t-th moment. The major semi-axis of the contact area at the t-th moment is used to calculate the lubrication traction force at the t-th moment; The calculation of the major semi-axis and minor semi-axis of the contact area at the t-th moment includes:

[0070]

[0071] where, is the major semi-axis of the contact area at the t-th moment, is the minor semi-axis of the contact area at the t-th moment, k is the ellipticity of the contact area, is k the second complete elliptic integral of is the equivalent curvature radius, is the contact stress at the t-th moment, is the equivalent elastic modulus.

[0072] By the above steps, the contact stress at the t-th moment, the major semi-axis of the contact area at the t-th moment and the traction coefficient are obtained, and a traction lubrication model is constructed. According to the contact stress at the t-th moment, the major semi-axis of the contact area at the t-th moment and the traction coefficient, the lubrication traction force at the t-th moment is calculated. The calculation formula is as follows:

[0073] Among them, is the lubrication traction force at the t-th moment, is the contact stress at the t-th moment, is the major semi-axis of the contact area at the t-th moment, is the traction coefficient.

[0074] S104. Obtain the interaction force and the moment of force at the t-th moment between the rolling ball and the raceway according to the contact stress and the lubrication traction force at the t-th moment.

[0075] Obtain the interaction force and the moment of force at the t-th moment between the rolling ball and the raceway according to the contact stress and the lubrication traction force at the t-th moment, including:

[0076] Among them, is the force exerted on the rolling ball by the raceway in the contact coordinate system of the rolling element and the inner and outer rings, is the lubrication traction force at the t-th moment, is the contact stress at the t-th moment; Among them, the moment of force at the t-th moment includes the moment of the rolling ball on the inner raceway and the moment of the raceway on the rolling ball. Calculate the moment of the rolling ball on the inner raceway through the following formula:

[0077] Calculate the moment of the raceway on the rolling ball through the following formula:

[0078] Among them, is the moment of the rolling ball on the inner raceway, is the position of the contact area of the rolling ball relative to the ball center in the rolling element orientation coordinate system, is the force exerted on the rolling ball by the raceway in the rolling element orientation coordinate system, is the moment of the raceway on the rolling ball, is the position of the contact point relative to the inner ring center in the inner ring fixed body coordinate system, is the force exerted on the raceway by the rolling ball in the inner ring fixed body coordinate system.

[0079] S105. Establish a dynamic modeling equation according to the interaction force and the moment of force at the t-th moment between the rolling ball and the raceway, and calculate the acceleration of the slewing bearing at the t-th moment according to the dynamic modeling equation.

[0080] Based on the interaction force and the moment of force at the t-th moment between the rolling ball and the raceway, a dynamic modeling equation is established. This dynamic modeling equation includes the motion equation of the center of mass of the raceway in the inertial coordinate system, the rotation equation of the inner ring in the fixed-body coordinate system of the inner ring, the translation equation of the rolling ball in the rolling body azimuth coordinate system, and the rotational equilibrium equation of the rolling ball.

[0081] The motion equation of the center of mass of the raceway in the inertial coordinate system is as follows:

[0082] The rotation equation of the inner ring in the fixed-body coordinate system of the inner ring is as follows:

[0083] The translation equation of the rolling ball in the rolling body azimuth coordinate system is as follows:

[0084] The rotational equilibrium equation of the rolling ball is as follows:

[0085] Among them, is the acceleration in the x direction of the slewing bearing, is the acceleration in the y direction of the slewing bearing, is the acceleration in the z direction of the slewing bearing, is the mass of the inner ring of the slewing bearing, is the axial load of the slewing bearing, is the radial load of the slewing bearing, is the x coordinate value of the force exerted on the raceway by the j-th rolling ball in the inertial coordinate system, is the y coordinate value of the force exerted on the raceway by the j-th rolling ball in the inertial coordinate system, is the z coordinate value of the force exerted on the raceway by the j-th rolling ball in the inertial coordinate system, , n is a positive integer, is the x coordinate value of the angular acceleration of the slewing bearing, is the y coordinate value of the angular acceleration of the slewing bearing, is the z coordinate value of the angular acceleration of the slewing bearing, is the y coordinate value of the moment exerted on the raceway by the rolling ball in the fixed-body coordinate system of the inner ring, is the z coordinate value of the moment exerted on the raceway by the rolling ball in the fixed-body coordinate system of the inner ring, is the component of the moment of inertia of the inner ring in the y direction, is the component of the moment of inertia of the inner ring in the z direction, is the acceleration of the rolling ball in the x direction, is the acceleration of the rolling ball in the r direction, is the acceleration of the rolling ball in the revolution direction, is the x - component of the force received by the rolling ball from the outer ring in the azimuth coordinate system, is the y - component of the force received by the rolling ball from the outer ring in the azimuth coordinate system, is the z - component of the force received by the rolling ball from the outer ring in the azimuth coordinate system, is the x - component of the force received by the rolling ball from the inner ring in the azimuth coordinate system, is the y - component of the force received by the rolling ball from the inner ring in the azimuth coordinate system, is the z - component of the force received by the rolling ball from the inner ring in the azimuth coordinate system, is the mass of the rolling ball, is the radius of the rolling ball, is the revolution speed of the rolling ball, is the x - component of the angular acceleration of the rolling ball, is the y - component of the angular acceleration of the rolling ball, is the z - component of the angular acceleration of the rolling ball, is the x - component of the torque received by the rolling ball from the inner ring in the azimuth system, is the y - component of the torque received by the rolling ball from the inner ring in the azimuth system, is the z - component of the torque received by the rolling ball from the inner ring in the azimuth system, is the x - component of the torque received by the rolling ball from the outer ring in the azimuth system, is the y - component of the torque received by the rolling ball from the outer ring in the azimuth system, is the z - component of the torque received by the rolling ball from the outer ring in the azimuth system, is the z - component of the angular velocity of the rolling ball's rotation, is the y - component of the angular velocity of the rolling ball's rotation, is the moment of inertia of the rolling ball.

[0086] S106. Determine whether the set duration is reached at the t - th moment.

[0087] Determine whether the set duration is reached at the t - th moment to obtain a first judgment result. If the first judgment result indicates that the set duration is reached at the t - th moment, then execute S107; If the first judgment result indicates that the set duration is not reached at the t - th moment, then execute S108.

[0088] The slewing bearing is a dynamic process in actual operation, and its motion state changes over time. By calculating up to a set time period, the motion conditions of the slewing bearing in various stages such as startup, acceleration, constant speed, deceleration, and stop within this time period can be completely described. For example, in the slewing bearing system of a crane, when the crane starts to rotate and lift a heavy object, the slewing bearing will have an acceleration process, then may maintain a constant speed during the rotation, and finally decelerate when stopping. Calculating the dynamic model within the set time period can accurately analyze key parameters such as the force, speed, and acceleration in each stage.

[0089] S107. Output the acceleration of the slewing bearing at the t-th moment and each moment before the t-th moment.

[0090] The slewing bearing will exhibit fatigue phenomena during long-term operation. Calculating the dynamic model for the set time period can analyze the stress changes of the slewing bearing during the repeated loading and unloading processes.

[0091] Therefore, when the set time period is reached, the fourth-order Runge-Kutta method is used to process the acceleration of the slewing bearing at the t-th moment to obtain the speed and displacement of the slewing bearing at the t-th moment, and the life prediction of the slewing bearing is carried out based on the speed and displacement.

[0092] The fourth-order Runge-Kutta method is a high-precision algorithm for solving the initial value problem of ordinary differential equations in numerical analysis. Its core idea is to approximate the solution of the differential equation through the weighted average of multi-stage slopes. Through the multi-stage slope estimation and weighted average strategy, high-precision solution is achieved on the premise of low computational resource consumption. It balances computational efficiency and accuracy.

[0093] S108. Calculate the acceleration of the slewing bearing at the (t + 1)-th moment.

[0094] Repeat the above steps to calculate the acceleration of the slewing bearing at the (t + 1)-th moment, which will not be elaborated here. Based on the above content, the present application provides a dynamic modeling method for the slewing bearing of an ultra-large aperture antenna. By combining theoretical derivation and numerical calculation, it can effectively reduce the calculation cost, and there is no need for expensive computing equipment and a large amount of computing time. This method can be implemented based on general mathematical calculation tools and programming languages, is not limited to specific finite element software, and improves the flexibility of research. Moreover, this method has a very low dependence on grids, avoiding errors and complexities caused by grid division problems, and making the research process more efficient.

[0095] The embodiment of the present application also provides a dynamic modeling device for the slewing bearing of an ultra-large aperture antenna, as Figure 3As shown in the figure, this is a schematic diagram of a dynamic modeling device for a slewing bearing of an extra-large aperture antenna provided by an embodiment of the present application. The device includes: an acquisition module 301, a calculation module 302, and a judgment module 303; The acquisition module 301 is configured to acquire the structural parameters of the slewing bearing in the antenna; The calculation module 302 is configured to calculate the contact stress at the t-th moment and the contact area at the t-th moment according to the structural parameters of the slewing bearing; calculate the lubrication traction force at the t-th moment between the rolling balls and the inner and outer raceways according to the contact stress at the t-th moment and the contact area at the t-th moment; obtain the interaction force at the t-th moment and the torque at the t-th moment between the rolling balls and the raceways according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment; establish a dynamic modeling equation according to the interaction force at the t-th moment and the torque at the t-th moment between the rolling balls and the raceways, and calculate the acceleration of the slewing bearing at the t-th moment according to the dynamic modeling equation; The judgment module 302 is configured to judge whether the t-th moment reaches a set duration, obtain a first judgment result. If the first judgment result indicates that the t-th moment reaches the set duration, output the acceleration of the slewing bearing at the t-th moment and each moment before the t-th moment.

[0096] In some possible implementation manners, the judgment module 302 is further configured to calculate the acceleration of the slewing bearing at the (t + 1)-th moment if the first judgment result indicates that the t-th moment does not reach the set duration.

[0097] In some possible implementation manners, the calculation module 302 is specifically configured to obtain the contact deformation amount between the rolling ball and the lower half circle of the inner raceway, and calculate the contact stress at the t-th moment according to the contact deformation amount between the rolling ball and the lower half circle of the inner raceway; The obtaining of the contact deformation amount between the rolling ball and the lower half circle of the inner raceway includes: Judging whether a first numerical value is greater than zero and whether the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring is less than zero, obtaining a first judgment result. If the first judgment result indicates that the first numerical value is greater than zero and the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring is less than zero, then determine that the first numerical value is the contact deformation amount between the rolling ball and the lower half circle of the inner raceway; The judgment is carried out through the following formula:

[0098]

[0099]

[0100] where is the contact deformation amount of the rolling ball and the lower half of the inner raceway, is the position of the curvature center of the raceway relative to the center of the rolling ball in the contact coordinate system, is the groove curvature coefficient of the lower half of the inner ring raceway, is the diameter of the rolling ball, is the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring, is the position of the center of the rolling ball in the fixed body coordinate system of the inner ring, is the position of the curvature center of the raceway in the fixed body coordinate system of the inner ring, is the x coordinate value of the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring; According to the contact deformation amount of the rolling ball and the lower half of the inner raceway and the Hertz contact theory, the contact stress at the t-th moment can be calculated.

[0101] In some possible implementation manners, the calculation module 302 is specifically configured to calculate the relative velocity of the raceway relative to the rolling ball at point p according to the contact area at the t-th moment, and then calculate the traction coefficient according to the relative velocity of the raceway relative to the rolling ball at point p, and calculate the lubricating traction force between the rolling ball and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the traction coefficient.

[0102] In some possible implementation manners, the calculation module 302 is specifically configured to:

[0103] wherein, is the force exerted on the rolling ball by the raceway in the contact coordinate system of the rolling element and the inner and outer rings, is the lubricating traction force at the t-th moment, is the contact stress at the t-th moment; wherein, the moment of force at the t-th moment includes the moment of the rolling ball by the inner raceway and the moment of the raceway by the rolling ball, and the moment of the rolling ball by the inner raceway is calculated by the following formula:

[0104] The moment of the raceway by the rolling ball is calculated by the following formula:

[0105] wherein, is the moment of the rolling ball by the inner raceway, is the position of the contact area of the rolling ball relative to the center of the ball in the rolling element azimuth coordinate system, is the force exerted on the rolling ball by the raceway in the rolling element azimuth coordinate system, is the moment of the raceway by the rolling ball, is the position of the contact point relative to the inner ring center in the fixed coordinate system of the inner ring. is the force exerted by the rolling ball on the raceway in the fixed coordinate system of the inner ring.

[0106] In some possible implementation manners, the calculation module 302 is further configured to calculate the major semi-axis of the contact area at the t-th moment according to the contact stress at the t-th moment, since the contact area at the t-th moment is elliptical. The major semi-axis of the contact area at the t-th moment is used to calculate the lubrication traction force at the t-th moment. Calculating the major semi-axis of the contact area at the t-th moment includes:

[0107] Wherein, is the major semi-axis of the contact area at the t-th moment, k is the ellipticity of the contact area, is k the complete elliptic integral of the second kind of is the equivalent curvature radius, is the contact stress at the t-th moment, is the equivalent elastic modulus.

[0108] In some possible implementation manners, the device further includes: Processing the acceleration of the slewing bearing at the t-th moment by using the fourth-order Runge-Kutta method to obtain the speed and displacement of the slewing bearing at the t-th moment, and predicting the life of the slewing bearing according to the speed and displacement.

[0109] The embodiment of the present application further provides a computing device. As Figure 4 shown, this figure is a schematic diagram of a computing device provided by the embodiment of the present application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other through the bus 401.

[0110] The bus 401 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of simplicity of representation, Figure 4 only a thick line is shown in

[0111] The processor 402 can be any one or more of processors such as a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0112] The communication interface 403 is used for external communication.

[0113] The memory 404 may include a volatile memory, such as a random access memory (RAM). The memory 404 may also include a non-volatile memory, such as a read-only memory (ROM), a flash memory, a hard disk drive (HDD), or a solid state drive (SSD).

[0114] Executable code is stored in the memory 404, and the processor 402 executes the executable code to perform the aforementioned dynamic modeling method for the slewing bearing of the super-large aperture antenna.

[0115] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state drive), etc. The computer-readable storage medium includes instructions that direct the computing device to execute the aforementioned dynamic modeling method for the slewing bearing of the super-large aperture antenna.

[0116] The embodiment of the present application also provides a computer program product, which includes one or more computer instructions. When the computer instructions are loaded and executed on a computing device, the processes or functions according to the embodiments of the present application are fully or partially generated.

[0117] The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, or data center to another website, computer, or data center by wire (such as coaxial cable, optical fiber) or wirelessly (such as infrared, wireless, microwave, etc.).

[0118] When the computer program product is executed by a computer, the computer executes any one of the methods of the above-mentioned swing bearing dynamics modeling method for the super-large aperture antenna. This computer program product can be a software installation package. In the case where any one of the methods of the above-mentioned swing bearing dynamics modeling method for the super-large aperture antenna is required, this computer program product can be downloaded and executed on the computer.

[0119] The descriptions of the processes or structures corresponding to the above-mentioned various drawings each have their own focuses. For parts not detailed in a certain process or structure, reference can be made to the relevant descriptions of other processes or structures.

[0120] As described above, this is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present application should be covered within the protection scope of the present application.

Claims

1. A dynamic modeling method for the slewing bearing of an extra-large aperture antenna, characterized in that The method includes: Obtaining the structural parameters of the slewing bearing in the antenna; Calculating the contact stress at the t-th moment and the contact area at the t-th moment according to the structural parameters of the slewing bearing; Calculating the lubrication traction force between the rolling balls and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the contact area at the t-th moment; Obtaining the interaction force at the t-th moment and the moment of force at the t-th moment between the rolling balls and the raceways according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment; Establishing a dynamic modeling equation according to the interaction force at the t-th moment and the moment of force at the t-th moment between the rolling balls and the raceways, and calculating the acceleration of the slewing bearing at the t-th moment according to the dynamic modeling equation; Judging whether the t-th moment reaches the set duration to obtain a first judgment result. If the first judgment result indicates that the t-th moment reaches the set duration, outputting the acceleration of the slewing bearing at the t-th moment and at each moment before the t-th moment.

2. The method according to claim 1, wherein The method further includes: If the first judgment result indicates that the t-th moment does not reach the set duration, calculating the acceleration of the slewing bearing at the (t + 1)-th moment.

3. The method according to claim 1, characterized in that, The calculating the contact stress at the t-th moment includes: Obtaining the contact deformation amount between the rolling ball and the lower half of the inner raceway, and calculating the contact stress at the t-th moment according to the contact deformation amount between the rolling ball and the lower half of the inner raceway; The obtaining the contact deformation amount between the rolling ball and the lower half of the inner raceway includes: Determine the first value whether it is greater than zero and whether the position vector of the contact point relative to the coordinate origin in the inner fixed body coordinate system is less than zero, to obtain a first judgment result. If the first judgment result indicates that the first value is greater than zero and the position vector of the contact point relative to the coordinate origin in the inner fixed body coordinate system is less than zero, then determine the first value as the contact deformation amount of the rolling ball and the lower half circle of the inner raceway; Judging through the following formula: Among them, is the contact deformation amount between the rolling ball and the lower half of the inner raceway, is the position of the curvature center of the raceway relative to the center of the ball of the rolling ball in the contact coordinate system, is the groove curvature coefficient of the lower half of the inner ring raceway, is the diameter of the rolling ball, is the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring, is the position of the center of the ball of the rolling ball in the fixed body coordinate system of the inner ring, is the position of the curvature center of the raceway in the fixed body coordinate system of the inner ring, is the x coordinate value of the position vector of the contact point relative to the coordinate origin in the fixed body coordinate system of the inner ring; According to the contact deformation amount between the rolling ball and the lower half of the inner raceway and the Hertz contact theory, the contact stress at the t-th moment can be calculated.

4. The method according to claim 1, wherein The calculating the lubrication traction force between the rolling balls and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the contact area at the t-th moment includes: Calculating the relative velocity of the raceway relative to the rolling ball at point p according to the contact area at the t-th moment, then calculating the traction coefficient according to the relative velocity of the raceway relative to the rolling ball at point p, and calculating the lubrication traction force between the rolling balls and the inner and outer raceways at the t-th moment according to the contact stress at the t-th moment and the traction coefficient.

5. The method according to claim 1, wherein The obtaining the interaction force at the t-th moment and the moment of force at the t-th moment between the rolling balls and the raceways according to the contact stress at the t-th moment and the lubrication traction force at the t-th moment includes: Among them, is the force exerted by the raceway on the rolling ball in the contact coordinate system of the rolling element and the inner and outer rings, is the lubrication traction force at the t-th moment, is the contact stress at the t-th moment; Wherein, the moment of force at the t-th moment includes the moment of the rolling ball on the inner raceway and the moment of the raceway on the rolling ball. The moment of the rolling ball on the inner raceway is calculated by the following formula: The moment of the raceway on the rolling ball is calculated by the following formula: wherein, is the moment of the rolling ball subjected to the inner raceway, is the position of the contact area of the rolling ball relative to the center of the ball in the rolling element orientation coordinate system, is the force exerted on the rolling ball by the raceway in the rolling element orientation coordinate system, is the moment of the raceway subjected to the rolling ball, is the position of the contact point p on the raceway relative to the center of the inner ring in the fixed body coordinate system of the inner ring, is the force exerted on the raceway by the rolling ball in the fixed body coordinate system of the inner ring.

6. The method according to claim 1, characterized in that, The method further includes: The contact area at the t-th moment is in an elliptical shape. Calculating the major semi-axis of the contact area at the t-th moment according to the contact stress at the t-th moment, and the major semi-axis of the contact area at the t-th moment is used to calculate the lubrication traction force at the t-th moment; The calculating the major semi-axis of the contact area at the t-th moment includes: Among them, is the major semi-axis of the contact area at the t-th moment, k is the ellipticity of the contact area, is k the complete elliptic integral of the second kind of is the equivalent curvature radius, is the contact stress at the t-th moment, is the equivalent elastic modulus.

7. The method according to claim 1, characterized in that The method further includes: Processing the acceleration of the slewing bearing at the t-th moment by using the fourth-order Runge-Kutta method to obtain the velocity and displacement of the slewing bearing at the t-th moment, and predicting the life of the slewing bearing according to the velocity and displacement.

8. A dynamic modeling device for the slewing bearing of an ultra-large aperture antenna, characterized in that, The device includes: An obtaining module, configured to obtain the structural parameters of the slewing bearing in the antenna; A calculation module, configured to calculate the contact stress and the contact area at the t-th moment according to the structural parameters of the slewing bearing; calculate the lubrication traction force at the t-th moment between the rolling balls and the inner and outer raceways according to the contact stress and the contact area at the t-th moment; obtain the interaction force and the acting moment at the t-th moment between the rolling balls and the raceways according to the contact stress and the lubrication traction force at the t-th moment; establish a dynamic modeling equation according to the interaction force and the acting moment at the t-th moment between the rolling balls and the raceways, and calculate the acceleration of the slewing bearing at the t-th moment according to the dynamic modeling equation. A judgment module, configured to judge whether the t-th moment reaches a set duration, obtain a first judgment result, and if the first judgment result indicates that the t-th moment reaches the set duration, output the acceleration of the slewing bearing at the t-th moment and at each moment before the t-th moment.

9. A computing device, characterized in that, It includes a memory and a processor; Wherein, one or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device is caused to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method according to any one of claims 1 to 7.

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