A method for modeling rotating error of close-coupled shafting under homogenization mechanism

Abstract

The application provides a modeling method for rotating error of dense bead shaft system under homogenization mechanism, and relates to the technical field of shaft system rotating error modeling. The modeling method for rotating error of dense bead shaft system under homogenization mechanism comprises the following steps: constructing an actual offset model of each row of balls, establishing a main shaft stress balance equation based on Hertz contact theory, combining the actual offset model of each row of balls with the main shaft stress balance equation based on Hertz contact theory to obtain a dense bead shaft system error homogenization coefficient; decomposing the main shaft error movement of the dense bead shaft system into pure radial movement and angular deflection movement, calculating the shaft center offset and the shaft line deflection angle; selecting a certain end face circle center as a calculation target, analyzing the movement position change of the circle center in the main shaft rotating process, and establishing a dense bead shaft system rotating error model. The method can accurately solve the dense bead shaft system error homogenization coefficient, quantitatively reveals the influence law of various factors of the component members on the rotating error, and provides a theoretical basis for the structure optimization design and precision improvement of the dense bead shaft system.

Description

Technical Field

[0001] This invention relates to the field of shaft rotation error modeling technology, specifically a method for modeling the rotation error of a dense bead shaft system under a homogenization mechanism. Background Technology

[0002] The ball bearing system is a core component of precision instruments, and its rotational accuracy directly affects the instrument's precision and performance. The ball bearing system employs an interference fit and has a large number of steel balls, allowing for improved rotational accuracy through error averaging. Currently, the structural design of ball bearing systems relies heavily on the experience of designers; improvements in their accuracy are still largely achieved by blindly increasing manufacturing precision, resulting in a lack of initiative and scientific rigor in their design and manufacturing. The error averaging mechanism of ball bearing systems remains unclear, the precise solution for the error averaging value has not been found, and the averaging effect has not been quantitatively analyzed, resulting in theoretical gaps that limit the application and promotion of ball bearing systems. Summary of the Invention

[0003] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a method for modeling the rotational error of a dense beaded shaft system under a homogenization mechanism. This method can accurately calculate the homogenization coefficient of the dense beaded shaft system error and quantitatively reveal the influence of various factors of the constituent components on the rotational error, providing a theoretical basis for the structural optimization design and accuracy improvement of the dense beaded shaft system.

[0004] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: Firstly, a method for modeling the rotational error of a densely beaded shaft system under a homogenization mechanism is provided, including: Construct an actual offset model for each row of balls, establish a spindle force balance equation based on Hertzian contact theory, and obtain the ball bearing system error equalization coefficient by combining the actual offset model for each row of balls with the spindle force balance equation based on Hertzian contact theory. The error motion of the main spindle of the decryption ball bearing system is divided into pure radial motion and angular runout motion. The spindle offset and axis runout angle are calculated. The center of the upper end face of the spindle is selected as the calculation target. The change in the position of the center during the rotation of the spindle is analyzed, and a rotation error model of the bead system is established. The influence of various error factors on the rotation error of the bearing system is revealed by using a model of the rotation error of the bearing system.

[0005] Preferably, the actual offset model for each column of balls is as follows: in, The outer diameter of the main spindle journal. This represents the actual offset of the spindle axis caused by the ball bearing error in the first column. For the first j The initial angle of the ball bearings; It is its first j The actual offset of the spindle axis caused by ball bearing error.

[0006] Preferably, the principal axis force balance equation based on Hertzian contact theory is as follows: in, M Here, n is the number of ball bearing rows, and n is the number of ball bearing rows in each quadrant. j The column number of the ball bearing. This is the initial interference. This refers to the Hertzian contact coefficient when the ball contacts the journal and bushing. The sum of the curvatures of the balls when they contact the journal. This represents the total error at the initial position of the first row of balls.

[0007] Preferably, the step of combining the actual offset model of each row of balls with the spindle force balance equation based on Hertzian contact theory to obtain the ball bearing system error averaging coefficient specifically includes: By combining the actual offset model of each row of balls with the spindle force balance equation based on Hertzian contact theory, we obtain the following... The resulting actual axial offset of the beaded bearing system Actual axial offset of the bead-retaining bearing system and number of ball bearing rows M Related to the definition of the bead-retaining shaft system error averaging coefficient : .

[0008] Preferably, the spindle error motion of the decomposition and decryption ball system consists of pure radial motion and angular runout motion. The calculation of the shaft center offset and shaft runout angle specifically includes: The spindle center offset and axis runout angle caused by spindle error motion are calculated using the full-point method. The full-point method includes calculating the first... j The ball with the largest total error among the ball bearings With the j The deflection angle caused by the error difference between all other balls in the column. And compare them, The ball bearing containing the minimum value is denoted as Using ball bearings Calculate the first j Shaft offset under pure radial motion caused by ball bearings, utilizing ball bearings and Calculate the axis deflection angle; Pure radial motion error is caused by the ball bearings Total error at Caused by, along the ball The offset in the radial direction, the total error causing the shaft center offset for: Calculation of angular yaw motion error: in, For the first j The yaw angle caused by the ball bearings. For the first j Ball bearings in column Total error at the location, For the first j Ball bearings in column Total error at the location, For the first j Ball bearings in column The row number it is in For the first j Ball bearings in column The row number it is in k For quadrant numbers, the value ranges from 1 to 4; Angular yaw error causes the spindle to rotate around the spindle. Contact points Yaw, contact point Calculation: in, , , Contact points along x , y , z The position coordinates of the direction, To maintain the center of the ball bearings in adjacent rows in the same column z Towards distance, Between the centers of two adjacent rows of ball bearings in the same row z Towards distance, This refers to the distance between the first row of the first ball and the top of the cage.

[0009] Preferably, the step of selecting the center of a certain end face as the calculation target, analyzing the change in the position of the center during the rotation of the main shaft, and establishing a rotation error model for the ball bearing system specifically includes: No. j Errors at the location of the ball bearings cause the center of a certain end face to be affected. The model for the change in point position and the amount of position change is as follows: in, The first j Caused by error at the position of the ball bearing Point edge x , y , z The change in position of direction They are respectively Point edge x , y , z Initial coordinates of direction; No. j The calculation of the rotational error of the ball bearing system caused by the ball bearings is as follows: in, R The radius of the largest circle at the apex; The rotational error model of the ball bearing system is established as follows: .

[0010] In a second aspect, a computer-readable storage medium is provided for storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the methods described.

[0011] Thirdly, a computing device is provided, comprising: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing any of the methods described.

[0012] (III) Beneficial Effects This invention provides a modeling method for the rotational error of a beaded bearing system under a homogenization mechanism. It accurately solves the error homogenization coefficient of the beaded bearing system and reveals the error homogenization mechanism of the beaded bearing system. The model can be used to quantitatively analyze the influence of various factors of the constituent components on the rotational error, making up for the deficiencies in the structural design theory and error homogenization mechanism of the beaded bearing system, and providing a theoretical basis for improving the rotational accuracy of the beaded bearing system. Attached Figure Description

[0013] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a flowchart illustrating the calculation of shaft rotation error in an embodiment of the present invention; Figure 3 This is a spindle offset diagram when errors exist in an embodiment of the present invention; Figure 4 This is a graph showing the changing trend of the error averaging coefficient and the number of ball bearing rows in an embodiment of the present invention; Figure 5 This is a schematic diagram of the radial bearing cage unfolded in an embodiment of the present invention; Figure 6 This is a top view of the radial bearing cage in an embodiment of the present invention; Figure 7 This is a graph showing the trend of the mean rotational error as a function of the number of ball bearing rows in an embodiment of the present invention. Figure 8 This is a graph showing the trend of the mean rotational error as a function of the ball bearing size error range in an embodiment of the present invention. Figure 9 This is a graph showing the trend of the mean slewing error as a function of the interference fit in an embodiment of the present invention. Detailed Implementation

[0014] The technical solutions in the embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0015] Example like Figure 1 As shown, this embodiment of the invention provides a method for modeling the rotational error of a dense beaded shaft system under a homogenization mechanism, comprising: Construct an actual offset model for each row of balls, establish a spindle force balance equation based on Hertzian contact theory, and obtain the ball bearing system error equalization coefficient by combining the actual offset model for each row of balls with the spindle force balance equation based on Hertzian contact theory. The error motion of the main spindle of the decryption ball bearing system is divided into pure radial motion and angular runout motion. The spindle offset and axis runout angle are calculated. The center of the upper end face of the spindle is selected as the calculation target. The change in the position of the center during the rotation of the spindle is analyzed, and a rotation error model of the bead system is established. The influence of various error factors on the rotation error of the bearing system is revealed by using a model of the rotation error of the bearing system.

[0016] See the attached flowchart for the calculation process of this method. Figure 2 As shown, the steps are as follows: First step, see appendix Figure 3 The total error at the initial position of the first row of balls (including ball size error, journal and bushing roundness error) is: The total error is positive, at which point the spindle axis shifts to the left by an amount of [missing information]. The actual offset model of each column of balls is obtained through the following formula: in, The outer diameter of the main spindle journal. This represents the actual offset of the spindle axis caused by the ball bearing error in the first column. The initial angle of the j-th ball bearing is shown in the appendix. Figure 6 ; It is the actual offset of the spindle axis caused by the ball bearing error in column j.

[0017] The second step, based on Hertz's contact theory, is that when the balls come into contact with the spindle or bushing, they undergo elastic deformation, generating a force on the spindle. After the spindle is subjected to the forces of all the balls, it reaches an equilibrium state. The force equilibrium equation of the spindle is constructed using the following formula: in, M Here, n is the number of ball bearing rows, and n is the number of ball bearing rows in each quadrant. j The column number of the ball bearing. This is the initial interference. This refers to the Hertzian contact coefficient when the ball contacts the journal and bushing. The sum of the curvatures of the balls when they contact the journal. This represents the total error at the initial position of the first row of balls.

[0018] The third step is to combine the actual offset model of each row of balls with the spindle force balance equation to obtain the error. The resulting actual axial offset of the beaded bearing system Its relationship with the number of ball bearing rows M related.

[0019] The fourth step is to define the error averaging coefficient of the dense bead shaft system. : Pick , , .when M When the value is between 1 and 15, the error averaging coefficient can be obtained according to the above formula. With the number of ball bearing rows M See attached chart for the relationship trend. Figure 4 As shown, the error averaging effect can be observed.

[0020] The fifth step is to determine the coordinate position of each ball.

[0021] Step 6: Compare the balls with the largest total error in each row of balls. The deflection angle caused by the error difference between the ball and all other balls in this column. And compare them, The ball bearing containing the minimum value is denoted as Then use ball bearings To calculate the first j Shaft offset under pure radial motion caused by ball bearings: Step 7: The angular yaw motion is caused by the inconsistent size of each type of ball bearing. This is addressed by utilizing the ball bearings... and The axis deflection angle is calculated using the following formula: in, For the first j The yaw angle caused by the ball bearings. For the first j Ball bearings in column Total error at the location, For the first j Ball bearings in column Total error at the location, For the first j Ball bearings in column The row number it is in For the first j Ball bearings in column The row number it is in k It is a quadrant number, with values ​​ranging from 1 to 4.

[0022] Step 8, the angular yaw error motion causes the main shaft to rotate around the main shaft and... Contact points Yaw, calculate the contact point Location coordinates: in: In the formula, These are the deflection points. along x , y , z The position coordinates of the direction, To maintain the center of the ball bearings in adjacent rows in the same column z Towards distance, Between the centers of two adjacent rows of ball bearings in the same row z Towards distance, This refers to the distance from the top of the cage to the first row of the first ball bearing. See Appendix. Figure 5 .

[0023] Step 9: Select the center of a circle on a certain end face. To calculate the objective, solve the problem by the first...j Error at the position of the ball bearings causes the tip to be at its highest point. Positional change: In the formula, Caused by error Point edge x , y , z The change in position of direction They are respectively Point edge x , y , z Initial coordinates of the direction.

[0024] Step 10, solve the... j Rotational error of the ball bearing system caused by the ball bearings: Step 11: Establish the rotational error model for the ball bearing system as follows: Based on the model, suggestions can be provided for the design of dense bead shaft systems.

[0025] See appendix Figure 7 The graph shows the trend of the mean rotational error calculated based on the model as a function of the number of ball rows. It is evident that the number of ball rows has a significant impact on rotational error. When the number of ball rows is 1-5, the rotational error decreases dramatically with increasing ball rows, indicating that the error averaging effect effectively suppresses the impact of rotational error on rotational accuracy. However, when the number of ball rows exceeds 6, the decrease in rotational error becomes less significant, especially when the number of ball rows exceeds 10, where the increase in ball rows has a negligible impact on rotational accuracy. Furthermore, as the number of balls increases, the frictional torque increases, reducing the flexibility and stability of the shaft system. Therefore, to balance shaft system accuracy with flexibility and stability, it is recommended that dense ball bearing shaft systems use 6-10 ball rows depending on the size.

[0026] See appendix Figure 8 The graph shows the trend of the mean rotational error calculated based on the model as a function of the ball bearing size error range; it can be seen that as the ball bearing error range increases... As the value increases, the average gyration error shows an overall linear upward trend, and It has a significant impact on rotational error. To ensure the rotational accuracy of the shaft system, the balls should be pre-selected and strictly controlled. Value, and choose ball bearings with high size consistency as much as possible.

[0027] See appendix Figure 9The figure shows the trend of the mean slewing error as a function of the interference fit, calculated according to the model. It can be seen that as the interference fit increases, the mean slewing error generally decreases, indicating that increasing the interference fit is beneficial for improving the spindle's slewing accuracy. At that time, as the interference increases, the slewing error tends to decrease significantly; however, when At this time, the rotational error tends to stabilize. Taking into account the accuracy requirements of the shaft system and the actual situation, it is recommended to select an interference fit of about 3~8μm according to the size and error of the ball bearings and shaft system.

[0028] The ball bearing system rotation error modeling method of the present invention can obtain a rotation error model under the error averaging mechanism. The model can reveal the influence law of various error factors of the bearing system on the rotation error, and then propose a strategy to ensure rotation accuracy. This provides designers with initiative and scientific basis for determining the optimization design principles and accuracy improvement of the ball bearing system.

[0029] Embodiments of this application may be provided as methods or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application may be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0030] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0031] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0032] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0033] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method for modeling the rotational error of a dense bead shaft system under a homogenization mechanism, characterized in that, include: Construct an actual offset model for each row of balls, establish a spindle force balance equation based on Hertzian contact theory, and obtain the ball bearing system error equalization coefficient by combining the actual offset model for each row of balls with the spindle force balance equation based on Hertzian contact theory. The error motion of the main spindle of the decryption ball bearing system is divided into pure radial motion and angular runout motion. The spindle offset and axis runout angle are calculated. The center of the upper end face of the spindle is selected as the calculation target. The change of the center's position during the spindle's rotation is analyzed, and a model of the rotation error of the bead system is established. The influence of various error factors on the rotation error of the bearing system is revealed by using a model of the rotation error of the bearing system. The process involves selecting the center of the upper end face of the spindle as the calculation target, analyzing the change in the position of the center during the spindle rotation, and establishing a rotation error model for the bead-retaining shaft system. Specifically, this includes: No. j Errors at the location of the ball bearings cause the center of a certain end face to be affected. The model for the change in point position and the amount of position change is as follows: in, The first j Caused by error at the position of the ball bearing Point edge x , y , z The change in position of direction; This is the error averaging coefficient for the dense bead shaft system; For the first j Ball bearings in column Total error at; For the first j The initial angle of the ball bearings; , , Contact points along x , y , z The position coordinates of the direction; For the first j The yaw angle caused by the ball bearings; They are respectively Point edge x , y , z Initial coordinates of direction; No. j The calculation of the rotational error of the ball bearing system caused by the ball bearings is as follows: in, R The radius of the largest circle at the apex; The rotational error model of the ball bearing system is established as follows: in, k is the quadrant number, with values ​​from 1 to 4; n is the number of ball rows in each quadrant; j is the number of the ball's column.

2. The method for modeling the rotational error of a dense bead shaft system under the homogenization mechanism according to claim 1, characterized in that: The actual offset model for each column of balls is as follows: in, The outer diameter of the main spindle journal. The actual offset of the ball bearing system's axis caused by the total error at the initial position of the first row of balls. For the first j The actual offset of the ball bearing shaft system caused by the total error at the initial position of the ball bearings.

3. The method for modeling the rotational error of a dense bead shaft system under the homogenization mechanism according to claim 2, characterized in that: The principal axis force balance equation based on Hertzian contact theory is as follows: in, M For the number of ball bearing rows, This is the initial interference. This refers to the Hertzian contact coefficient when the ball contacts the journal and bushing. The sum of the curvatures of the balls when they contact the journal. This represents the total error at the initial position of the first column of balls.

4. The method for modeling the rotational error of a dense bead shaft system under the homogenization mechanism according to claim 3, characterized in that: The method combines the actual offset model of each ball bearing row with the spindle force balance equation based on Hertzian contact theory to obtain the error averaging coefficient of the ball bearing shaft system, specifically including: By combining the actual offset model of each row of balls with the spindle force balance equation based on Hertzian contact theory, we obtain the following... The resulting actual axial offset of the beaded bearing system Actual axial offset of the bead-retaining bearing system and number of ball bearing rows M Related to the definition of the bead-retaining shaft system error averaging coefficient : 。 5. The method for modeling the rotational error of a dense bead shaft system under the homogenization mechanism according to claim 4, characterized in that: The spindle error motion of the decomposition and decryption ball system consists of pure radial motion and angular runout motion. The calculation of the spindle offset and axis runout angle specifically includes: The spindle center offset and axis runout angle caused by spindle error motion are calculated using the full-point method. The full-point method includes calculating the first... j The ball with the largest total error in the ball bearing column With the j The deflection angle caused by the error difference between all other balls in the column. And compare them, The ball bearing containing the minimum value is denoted as Using ball bearings Calculate the first j Shaft offset under pure radial motion caused by ball bearings, utilizing ball bearings and Calculate the axis deflection angle; Pure radial motion error is caused by the ball bearings Total error at Caused by, along the ball The offset in the radial direction, the total error causing the shaft center offset for: Calculation of angular yaw motion error: in, For the first j The yaw angle caused by the ball bearings. For the first j Ball bearings in column Total error at the location, For the first j Ball bearings in column The row number it is in For the first j Ball bearings in column The row number it is in; Angular yaw error causes the spindle to rotate around the spindle. Contact points Yaw, contact point Calculation: in, To maintain the center of the ball bearings in adjacent rows in the same column z Towards distance, Between the centers of two adjacent rows of ball bearings in the same row z Towards distance, This refers to the distance between the first row of the first ball and the top of the cage.

6. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any of the methods according to claims 1-5.

7. A computing device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods according to claims 1-5.

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