A method of automatically centering and assembling bearings on long shaft parts

Abstract

The application provides a method for automatically centering and assembling bearings on long shaft parts, and belongs to the technical field of bearing assembly. The position information of the long shaft part and the bearing is collected in real time by a binocular camera and a laser ranging sensor, the least square method is used to calculate the center line equation and determine the position deviation, the centering adjustment vector is generated to control the multi-degree-of-freedom precise pose adjustment platform to perform preliminary adjustment, a mechanical arm is used to cooperate with high-precision laser ranging to perform accurate centering, the centering process is modeled as a weighted undirected graph and the optimal adjustment path is solved, the best pressing parameters are calculated based on the physical mechanics equation of bearing pressing to perform pressing, the assembly process is monitored through a force sensor and a displacement sensor, an assembly quality evaluation matrix is constructed, and finally the assembly result is detected and evaluated, so that high-precision automatic assembly of the long shaft part and the bearing is realized.

Description

Technical Field

[0001] This invention belongs to the field of bearing assembly technology, and more specifically, relates to a method for automatically aligning and assembling bearings on long shaft parts. Background Technology

[0002] Precision assembly of long shaft components and bearings is a key process in the machinery manufacturing industry, traditionally relying mainly on manual experience or semi-automated equipment for alignment and press-fitting. In fields such as precision machinery, aerospace, and heavy machinery, the assembly accuracy of long shaft components and bearings directly affects the overall performance and service life of the machine. Currently widely used methods include manual visual alignment, mechanical limit alignment, and basic vision-guided assembly technologies, which have been successfully applied in simple industrial scenarios.

[0003] However, traditional technologies have significant drawbacks: manual alignment is limited by operator experience, resulting in high subjectivity, low efficiency, and poor consistency; mechanical limit alignment is ill-suited to different parts specifications and lacks flexibility; while basic vision-guided technology can provide some positional information, it lacks a real-time feedback and adjustment mechanism, making it unable to cope with dynamic changes during assembly. More importantly, existing technologies generally lack a quality monitoring and evaluation system for the entire assembly process, making it difficult to detect and correct assembly abnormalities in a timely manner.

[0004] Faced with the growing demand for high-precision and high-reliability assembly, the core problem that traditional technologies struggle to solve is how to achieve high-precision real-time alignment of long-shaft parts and bearings under six degrees of freedom in space. This problem is particularly prominent in fields such as high-end equipment manufacturing and precision instrument production, and urgently requires breakthroughs in new intelligent assembly technologies. Summary of the Invention

[0005] In view of this, the present invention provides a method for automatically aligning and assembling bearings on long shaft parts, which can solve the technical problem in the prior art where the real-time positional relationship between long shaft parts and bearings is difficult to measure and adjust accurately, resulting in low assembly accuracy.

[0006] This invention is implemented as follows: It provides a method for automatically aligning and assembling bearings on long-shaft parts. The method includes: acquiring real-time images of the long-shaft part and the bearing using a binocular camera to obtain image acquisition data and determine the deviation data between the long-shaft part and the bearing; generating an alignment adjustment vector set based on the deviation data and controlling a multi-degree-of-freedom precision attitude adjustment platform to perform preliminary position adjustment; using a robotic arm to bring the long-shaft part close to the bearing, while simultaneously monitoring the relative position in real time using a high-precision laser rangefinder; modeling the alignment process as a weighted undirected graph minimum spanning tree problem, solving the minimum spanning tree using the Kruskal algorithm to obtain the optimal adjustment path data, and achieving precise alignment; calculating the pressing parameters based on the bearing pressing physical and mechanical equations, and starting the hydraulic pressing mechanism for pressing.

[0007] The step of acquiring real-time images of the long shaft parts and bearings using a binocular camera to obtain image acquisition data further includes: determining the initial position state of the long shaft parts and bearings, and constructing the Euler angle matrix for the centering process and the Euler angle matrix for the centering deviation.

[0008] The centering process Euler angle matrix describes the relative attitude of the long shaft part and the bearing in three-dimensional space. It represents the spatial relationship between the two by rotation angle and includes three components: pitch angle, yaw angle and roll angle. It is used to accurately describe the relative position state of the two parts during the assembly process.

[0009] The alignment deviation Euler angle matrix represents the angular difference between the ideal and actual assembly positions of the long shaft parts and bearings. It consists of angular deviations in three directions and is used to calculate the angular parameters that need to be adjusted.

[0010] The determination of the deviation data between the long shaft component and the bearing further includes: determining the positional deviation data and the angular deviation data, and constructing the axial change matrix and the radial change matrix.

[0011] The axial change matrix describes the displacement adjustment required for the long shaft component along its axial direction, including the positional changes of multiple feature points on the axis, and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform axial adjustment.

[0012] The radial change matrix describes the displacement adjustment required for the long axis component in the direction perpendicular to its axis, including the displacement in the horizontal and vertical directions, and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform radial adjustment.

[0013] The centering adjustment vector set is a set of three-dimensional adjustment vectors calculated based on the position deviation data and the angle deviation data. It includes the adjustment direction and the adjustment amount and is used to control the multi-degree-of-freedom precision attitude adjustment platform to perform precise adjustment actions.

[0014] The step of monitoring the relative position in real time using a high-precision laser rangefinder further includes: constructing a real-time alignment matching matrix. This real-time alignment matching matrix is ​​a data matrix dynamically constructed during the assembly process that reflects the real-time relative positional relationship between the long shaft parts and the bearings. It is updated in real time through feedback data from the high-precision laser rangefinder to precisely control the alignment process.

[0015] The precise alignment further includes: constructing an optimal alignment position matrix, which describes the spatial relationship data set when the long shaft parts and bearings reach the optimal assembly position, serving as the trigger condition and benchmark for the press-fitting operation, and ensuring that press-fitting is performed under the optimal alignment state.

[0016] This invention achieves intelligent control of the entire process from centering and positioning to press-fitting. The method constructs a complete spatial position perception system using a binocular camera and a high-precision laser rangefinder. Combined with mathematical models such as Euler angle matrices and the least squares method, it accurately describes the spatial positional relationship between long shaft parts and bearings, providing a precise basis for real-time adjustments.

[0017] Compared to traditional technologies, this invention significantly improves assembly accuracy and consistency: First, by modeling the alignment process as a weighted undirected graph minimum spanning tree problem and applying Kruskal's algorithm to find the optimal adjustment path, alignment efficiency and accuracy are greatly improved. Second, by calculating the optimal pressing parameters based on physical mechanics equations and combining them with real-time force-displacement monitoring, the pressing process is ensured to meet theoretical expectations. Finally, a systematic assembly quality evaluation system is established, using assembly quality evaluation functions to analyze real-time data, enabling quality monitoring and evaluation of the assembly process. This solves the technical problem of low assembly accuracy caused by the difficulty in accurately measuring and adjusting the real-time positional relationship during the precision alignment and assembly of medium and long shaft parts and bearings in existing technologies. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0020] like Figure 1 The diagram shows a flowchart of a method for automatically aligning and assembling bearings on a long shaft part according to the present invention. This method includes the following steps:

[0021] S01. Real-time image acquisition of the long shaft parts and bearings is performed using a binocular camera to obtain image acquisition data, determine the initial position state of the long shaft parts and bearings, and construct the Euler angle matrix for the centering process and the Euler angle matrix for the centering deviation.

[0022] S02. Based on the image acquisition data, the centerline equations of the long shaft part and the bearing are calculated using the least squares method, and axial change matrix and radial change matrix are constructed to determine the positional deviation data and angular deviation data between the long shaft part and the bearing.

[0023] S03. Based on the position deviation data and the angle deviation data, and combined with the preset accuracy requirement data, generate a centering adjustment vector set, and control the multi-degree-of-freedom precision attitude adjustment platform to perform preliminary position adjustment so that the long shaft parts and bearings reach the pre-centering state.

[0024] S04. A robotic arm is used to slowly approach the bearing with the long shaft part, while a high-precision laser rangefinder sensor monitors the relative position data between the long shaft part and the bearing in real time to build a real-time alignment and matching matrix.

[0025] S05. Based on the real-time alignment matching matrix feedback data, the alignment process is modeled as a weighted undirected graph minimum spanning tree problem, where nodes represent adjustment states and edge weights represent adjustment costs. The minimum spanning tree is solved using the Kruskal algorithm to obtain the optimal adjustment path data. The multi-degree-of-freedom precision attitude adjustment platform is controlled to make precise adjustments along the optimal adjustment path data to achieve precise alignment of the long shaft parts and bearings, and to construct the optimal alignment position matrix.

[0026] S06. After achieving precise alignment, calculate the optimal pressing parameters based on the physical and mechanical equations of bearing pressing. The bearing inner diameter data, shaft outer diameter data, bearing material elastic modulus data, shaft material elastic modulus data, and contact surface friction coefficient data are used as input parameters. Output the optimal pressing force and pressing speed curve data, start the hydraulic pressing mechanism, and press the bearing smoothly onto the long shaft part along the axial direction.

[0027] S07. During the press-fitting process, force sensors and displacement sensors continuously monitor assembly force data and displacement data, constructing a real-time dataset of the assembly force data and displacement data. The assembly quality evaluation function is used to analyze the real-time dataset, wherein the input parameters of the assembly quality evaluation function include the real-time dataset, standard force-displacement curve parameter data, bearing material elastic modulus data, shaft material elastic modulus data, and ambient temperature factor data. The output is assembly quality score data and abnormal state judgment result data, constructing an assembly process quality evaluation matrix.

[0028] S08. Optionally, after assembly is completed, the binocular camera is restarted to detect the assembly result, calculate the concentricity error data after assembly, determine whether the concentricity error data meets the assembly accuracy requirements, and output an assembly quality assessment report based on the assembly quality score data, the abnormal state judgment result data, and the concentricity error data.

[0029] Among them, the Euler angle matrix of the centering process is a mathematical model that describes the relative attitude of the long shaft parts and the bearing in three-dimensional space. It represents the spatial relationship between the two by rotation angles and includes three components: pitch angle, yaw angle and roll angle. It is used to accurately describe the relative position state of the two parts during the assembly process.

[0030] The centering deviation Euler angle matrix is ​​specifically a matrix representing the angular difference between the ideal and actual assembly positions of the long shaft parts and bearings. It consists of angular deviations in three directions and is used to calculate the angular parameters that need to be adjusted.

[0031] The axial change matrix is ​​a mathematical model that describes the displacement adjustment required for the long shaft part along its axial direction. It includes the positional changes of multiple feature points on the axis and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform axial adjustment.

[0032] Specifically, the radial change matrix is ​​a mathematical model that describes the displacement adjustment required for the long shaft part in the direction perpendicular to its axis. It includes the displacement in the horizontal and vertical directions and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform radial adjustment.

[0033] Specifically, the real-time alignment matching matrix is ​​a data matrix dynamically constructed during the assembly process that reflects the real-time relative positional relationship between the long shaft parts and the bearings. It is updated in real time through feedback data from the high-precision laser rangefinder sensor and is used to precisely control the alignment process.

[0034] The optimal alignment position matrix is ​​a set of spatial relationship data describing the optimal assembly position of the long shaft parts and bearings. It serves as the triggering condition and benchmark for the press-fitting operation, ensuring that press-fitting is performed under the optimal alignment condition.

[0035] Specifically, the centering adjustment vector set is a set of three-dimensional adjustment vectors calculated based on the position deviation data and the angle deviation data, including the adjustment direction and adjustment amount, used to control the multi-degree-of-freedom precision attitude adjustment platform to perform precise adjustment actions.

[0036] Specifically, the assembly process quality assessment matrix is ​​a data matrix that records the relationship between the assembly force data and the displacement data during the pressing process. By analyzing the curve feature points and curve shape of the assembly force data and the displacement data, it is determined whether the pressing process meets the quality requirements.

[0037] Among them, the physical and mechanical equation of bearing press fitting is a mathematical model based on the theory of elasticity to describe the mechanical behavior of bearing and shaft during the fit process. It takes into account factors such as material elastic deformation, frictional resistance, and thermal expansion effect, and is used to predict the stress distribution and deformation during the press fitting process, and to determine the optimal press fitting force and press fitting speed curve data.

[0038] Specifically, the assembly quality assessment function is a mathematical model based on real-time data analysis. By comparing the differences between the real-time dataset and the standard force-displacement curve parameter data, and combining the influence of the bearing material elastic modulus data, the shaft material elastic modulus data, and the environmental temperature factor data, the assembly quality score data and the abnormal state judgment result data are calculated to provide real-time quality monitoring and assessment for the assembly process.

[0039] Specifically, the optimal adjustment path data is obtained by solving the minimum spanning tree problem of a weighted undirected graph using the Kruskal algorithm, which yields the best adjustment sequence from the initial state to the target state, minimizing the time and energy consumption during the adjustment process and improving the centering efficiency.

[0040] Specifically, the preset accuracy requirements refer to the alignment accuracy standards between the long shaft parts and the bearings set in advance during the assembly process, including radial deviation limits, axial deviation limits and angular deviation limits, which serve as benchmark parameters for judging the alignment quality.

[0041] Specifically, the bearing inner diameter data refers to the actual measured value of the inner diameter of the bearing to be assembled, which is obtained by a precision measuring instrument and is used as input for calculating the physical and mechanical equations of bearing press fitting.

[0042] Specifically, the shaft outer diameter data refers to the actual measured value of the outer diameter of the bearing assembly part on the long shaft part, which is obtained by a precision measuring instrument and is used as the input for calculating the physical and mechanical equations of bearing press fitting.

[0043] The contact surface friction coefficient data specifically refers to the friction coefficient value between the inner surface of the bearing and the outer surface of the long shaft part. It is affected by factors such as material type, surface roughness, and lubrication status, and is obtained through friction testing instruments. It is used as input for calculating the physical and mechanical equations of bearing press fitting.

[0044] The standard force-displacement curve parameter data specifically refers to the standard parameter set of the force-displacement relationship during the bearing press-fitting process under ideal assembly conditions, including the initial force value during press-fitting, the force growth rate during press-fitting, and the force value at key displacement points, which serve as a reference benchmark for evaluating the actual assembly quality.

[0045] Among them, the ambient temperature factor data specifically refers to the numerical parameters of the influence of ambient temperature on the thermal expansion of materials during the assembly process. These parameters are measured in real time by temperature sensors and are used to consider the impact of temperature on the assembly process in the assembly quality assessment.

[0046] The specific implementation methods of the above steps are described in detail below.

[0047] The specific implementation of step S01 involves acquiring multi-angle images of the long-shaft part and bearing using an industrial-grade binocular camera. The acquisition frequency is set to 25 frames per second to ensure real-time dynamic image data. The binocular camera employs the principle of stereo vision, simultaneously imaging the same scene through two cameras at different positions, and calculating the three-dimensional spatial information of the target object using the principle of parallax. During image acquisition, the camera resolution is set to 1920×1080 pixels, and an adaptive exposure algorithm is used to ensure image clarity. After preprocessing, the contour features of the long-shaft part and bearing are extracted. Based on the extracted feature point coordinate data, a spatial coordinate transformation algorithm is used to calculate the position and attitude of the long-shaft part and bearing in the world coordinate system. The Euler angle matrix for the alignment process is calculated by extracting the axial direction vectors of the long-shaft part and bearing, including three components: pitch angle, yaw angle, and roll angle, with angular accuracy controlled within 0.01°. The alignment deviation Euler angle matrix is ​​calculated by comparing the actual Euler angles with the target Euler angles under ideal assembly conditions, serving as the basis for subsequent adjustments. The purpose of this step is to establish an accurate mathematical model of the initial position of the long shaft parts and bearings, providing basic data support for the subsequent alignment process.

[0048] The specific implementation of step S02 is based on the image acquisition data obtained in step S01. First, image segmentation processing is performed to separate the long shaft part and bearing area from the background. An edge detection algorithm is used to extract feature point sets of the outer contour line of the long shaft part and the inner contour line of the bearing, with no less than 50 feature points extracted for each contour. A least squares fitting algorithm is applied to these feature points to construct the centerline equations of the long shaft part and the bearing. The centerline equations are represented by parametric straight lines, i.e., x = x0 + at, y = y0 + bt, z = z0 + ct, where (x0, y0, z0) are the coordinates of a point on the line, and (a, b, c) are the direction vectors of the line. By comparing the relative positional relationship between the centerline of the long shaft part and the centerline of the bearing, an axial change matrix and a radial change matrix are constructed. The axial change matrix describes the deviation data in the direction of the long shaft axis, including the positional changes of at least 5 key feature points on the axis. The radial change matrix describes the horizontal and vertical deviations perpendicular to the axis, recorded in micrometers. The positional and angular deviations between the long shaft component and the bearing are calculated through mathematical transformations. Positional deviations include linear displacements in the x, y, and z directions, while angular deviations include rotational angles around the x, y, and z axes. The purpose of this step is to accurately quantify the positional and angular deviations between the long shaft component and the bearing, providing precise data for subsequent alignment adjustments.

[0049] The specific implementation of step S03 involves generating an alignment adjustment vector set based on the position and angle deviation data calculated in step S02, combined with preset accuracy requirements. The preset accuracy requirements include a radial deviation limit of no more than 5 μm, an axial deviation limit of no more than 10 μm, and an angle deviation limit of no more than 0.005°. The alignment adjustment vector set is represented by a six-dimensional vector, containing three displacement components and three rotational components, each corresponding to a specific adjustment direction and amount. The vector set is generated using a gradient descent algorithm, iteratively optimizing to find the optimal adjustment parameters to minimize the alignment deviation. Based on the alignment adjustment vector set data, the system controls a multi-degree-of-freedom precision attitude adjustment platform to perform preliminary position adjustments. This attitude adjustment platform employs a six-axis parallel mechanism design, possessing three translational degrees of freedom and three rotational degrees of freedom, achieving a positioning accuracy of 0.1 μm and an angle adjustment accuracy of 0.001°. When the attitude adjustment platform performs adjustments, a step-by-step adjustment strategy is adopted: first, coarse adjustments are performed to eliminate most deviations, followed by fine adjustments to achieve the preset accuracy requirements, ensuring that the long-axis parts and bearings reach a pre-aligned state. The purpose of this step is to adjust the long shaft parts and bearings to a pre-aligned state that meets the preset accuracy requirements, thus creating conditions for subsequent precise alignment operations.

[0050] The specific implementation of step S04 involves using a six-degree-of-freedom robotic arm to control the long shaft part to slowly approach the bearing. The robotic arm employs a servo control system, with its movement speed set to no more than 5 mm / s to ensure a smooth and controllable approach process. Simultaneously, at least three high-precision laser rangefinders are deployed, with a measurement accuracy of no less than 0.5 μm and a sampling frequency of no less than 1000 Hz, evenly distributed at 120° around the bearing to monitor the relative position data between the long shaft part and the bearing in real time. The laser rangefinders utilize the triangulation principle, calculating the target distance by measuring the time or angle of laser reflection back to the sensor. The sensor data is processed using a Kalman filter algorithm to eliminate the influence of random noise on measurement accuracy. Based on the real-time data from the three rangefinders, the system constructs a real-time alignment matching matrix. This matrix is ​​a 4×4 homogeneous transformation matrix, containing both a rotation matrix and a translation vector, fully describing the spatial relationship between the long shaft part and the bearing. The real-time alignment matching matrix is ​​updated at a frequency of 100 Hz to ensure the system can respond promptly to position changes. The purpose of this step is to achieve a precise approach between the long shaft parts and the bearing, and to monitor the relative positional relationship in real time using a high-precision sensor, providing data support for subsequent precise alignment adjustments.

[0051] The specific implementation of step S05 involves establishing a centering adjustment state space based on the real-time centering matching matrix feedback data obtained in step S04. The centering process is modeled as a weighted undirected graph minimum spanning tree problem, where each node represents an adjustment state, with a total of at least 100 nodes covering key state points in the adjustment process. Edges between nodes represent adjustment operations from one state to another, and the edge weight represents the comprehensive cost of the adjustment operation, including the weighted sum of time consumption, energy consumption, and adjustment difficulty coefficient. The weight calculation formula is w = αT + βE + γD, where T is time consumption, E is energy consumption, D is the difficulty coefficient, and α, β, and γ are the corresponding weight coefficients, with values ​​ranging from [0.4, 0.5], [0.3, 0.4], and [0.1, 0.3], respectively. Based on the constructed weighted undirected graph, the Kruskal algorithm is applied to solve for the minimum spanning tree. The Kruskal algorithm is based on a greedy strategy, selecting edges in ascending order of weight while avoiding loops, ultimately generating a minimum weight spanning tree containing all nodes. By analyzing the structure of the spanning tree, the system obtains the optimal adjustment path data from the initial state to the target state. This path data includes a sequence of adjustment actions and their corresponding parameter values. The system controls a multi-degree-of-freedom precision attitude adjustment platform to make precise adjustments along the optimal adjustment path data. The adjustment process employs a closed-loop control strategy, detecting the adjustment effect in real time and making compensation corrections, ultimately achieving precise alignment of the long shaft part and the bearing, and constructing an optimal alignment position matrix. This matrix records the position parameters of the long shaft part and the bearing when they reach the optimal assembly state, serving as the reference data for subsequent press-fitting operations. The purpose of this step is to solve for the optimal adjustment path using an optimization algorithm, achieving high-precision alignment of the long shaft part and the bearing, and creating optimal initial conditions for subsequent press-fitting operations.

[0052] The specific implementation of step S06 involves calculating the optimal pressing parameters based on the physical and mechanical equations of bearing pressing after achieving precise alignment. First, input parameters are read, including the bearing inner diameter, shaft outer diameter, bearing material elastic modulus, shaft material elastic modulus, and contact surface friction coefficient. The mechanical behavior during bearing pressing conforms to elasticity theory, and there is a nonlinear relationship between the pressing force F and the interference fit δ, contact surface area S, material elastic modulus E, and friction coefficient μ. An improved elasticity model is used to calculate the pressing force, considering material deformation, contact friction, and thermal expansion effects. Numerical solutions are used to obtain the pressing force values ​​at different pressing depths, forming force-displacement curves. The optimal pressing force range is determined based on the bearing size. For bearings with a diameter less than 50mm, the pressing force is controlled within the range of 2000N to 5000N; for bearings with a diameter between 50mm and 100mm, the pressing force is controlled within the range of 5000N to 10000N; and for bearings with a diameter greater than 100mm, the pressing force is controlled within the range of 10000N to 20000N. The pressing speed curve adopts a segmented control strategy: the initial contact stage speed is set to 0.5mm / s, the main pressing stage speed is 1mm / s, and the final positioning stage speed is reduced to 0.2mm / s, ensuring a smooth and controllable pressing process. The system controls the hydraulic pressing mechanism based on the calculation results to smoothly press the bearing onto the long shaft part along the axial direction. The hydraulic pressing mechanism uses a high-precision servo control system, with a pressure control accuracy of no less than 0.5% and a displacement control accuracy of no less than 1μm. The purpose of this step is to calculate the optimal pressing parameters based on physical and mechanical principles to ensure a smooth and controllable bearing pressing process and avoid problems such as incomplete pressing or excessive pressing.

[0053] The specific implementation of step S07 involves continuously monitoring assembly force and displacement data during the press-fitting process using force and displacement sensors. The force sensor employs a piezoelectric design, with a measurement range of 0–50 kN, an accuracy of no less than 0.1%, and a sampling frequency of no less than 1000 Hz. The displacement sensor employs a capacitive design, with a measurement range of 0–50 mm, an accuracy of no less than 0.1 μm, and a sampling frequency of no less than 1000 Hz. The system collects sensor data in real time, constructing a real-time dataset of assembly force and displacement data, updating 1000 sampling points per second. Based on the real-time dataset, the system uses an assembly quality evaluation function for analysis. This evaluation function employs a multi-parameter weighted evaluation model, with input parameters including the real-time dataset, standard force-displacement curve parameters, bearing material elastic modulus data, shaft material elastic modulus data, and environmental temperature factor data. The evaluation function comprehensively evaluates assembly quality by comparing the deviation between the actual force-displacement curve and the standard curve, combined with the influence of material parameters and environmental factors. The evaluation indicators include curve shape similarity, key feature point deviation, and curve slope change, with each indicator assigned a different weight coefficient ranging from [0.1, 0.5]. The evaluation results output assembly quality score data and abnormal state judgment data. The assembly quality score uses a 100-point scale, with 90 points or above considered excellent, 75-90 points considered acceptable, and below 75 points considered unacceptable. Abnormal state judgment results include three levels: normal, minor abnormality, and severe abnormality, each corresponding to different handling measures. Based on the evaluation results, the system constructs an assembly process quality evaluation matrix. This matrix records key feature data on the force and displacement relationship during the pressing process, used for the final evaluation of assembly quality. The purpose of this step is to monitor key parameters during the pressing process in real time, promptly detect abnormalities, and ensure assembly quality.

[0054] Step S08 is optional. Specifically, after assembly, the binocular camera is restarted to inspect the assembly result. The camera acquires images of the assembled long-shaft parts and bearings at the same resolution as in step S01 to ensure inspection accuracy. The system processes the acquired images, extracts the contour features of the long-shaft parts and bearings, and calculates the concentricity error data after assembly. The concentricity calculation uses the least squares method to fit the center coordinates of the circle, and then calculates the deviation between the shaft and the bearing centerline. The concentricity error data includes radial deviation and angular deviation. The system determines whether the concentricity error data meets the assembly accuracy requirements. The assembly accuracy requirements are determined based on the bearing dimensions. For precision bearings, the concentricity error should not exceed 2μm; for ordinary bearings, the concentricity error should be controlled within 5μm. The system combines the assembly quality score data, abnormal state judgment results data, and concentricity error data to generate an assembly quality assessment report. The assessment report includes assembly parameter records, quality scores, abnormal state descriptions, concentricity error analysis, and improvement suggestions, providing data support for subsequent assembly process optimization. The purpose of this step is to conduct a final inspection of the assembly results, confirm whether the assembly quality meets the requirements, and generate a complete quality assessment report to provide a basis for continuous improvement of the assembly process.

[0055] The method of this invention models the alignment process as a weighted undirected graph minimum spanning tree problem and applies Kruskal's algorithm to solve for the optimal adjustment path, thereby achieving high-precision automatic alignment and assembly of long shaft parts and bearings. The entire method integrates technologies from multiple fields such as computer vision, precision measurement, optimization algorithms, and mechanical control, realizing automation, intelligence, and high precision in the assembly process, significantly improving the efficiency and quality of long shaft part bearing assembly.

[0056] The mathematical model or calculation process involved in this invention will be described in detail below.

[0057] In step S01, the calculation of the Euler angle matrix during the centering process is specifically represented as follows:

[0058] R = R z (γ)·R y (β)·R x (α);

[0059] In the formula, R is the Euler angle matrix for the centering process; R x (α) is the rotation matrix for rotating about the x-axis by an angle α (pitch angle); R y (β) is the rotation matrix for rotating about the y-axis by an angle β (yaw angle); R z (γ) is the rotation matrix for rotating about the z-axis by an angle γ (roll angle).

[0060] The specific matrix expansion form is as follows:

[0061]

[0062] The parameter acquisition method is as follows: pitch angle α, yaw angle β, and roll angle γ are extracted from image data acquired by a binocular camera. First, the feature point set of the long shaft parts and bearings is extracted using image processing algorithms. Then, 3D reconstruction technology is used to determine the position of the feature points in the spatial coordinate system. Finally, the axis direction vector is calculated based on the spatial distribution of the feature points, thereby obtaining the Euler angle parameters. The angle values ​​are typically within the range of -π / 2 ≤ α, β, γ ≤ π / 2, with an accuracy controlled within 0.01°.

[0063] The calculation of the Euler angle matrix for the mean deviation is specifically expressed as follows:

[0064]

[0065] In the formula, ΔR is the Euler angle matrix of the centering deviation; R target R is the Euler angle matrix in the target assembly state; actual This is the Euler angle matrix as measured in practice; For R target The inverse matrix.

[0066] The formula for extracting the deviation angle from the centering deviation Euler angle matrix is ​​as follows:

[0067] Δα=arctan2(r 32 r 33 );

[0068] Δβ=arcsin(-r 31 );

[0069] Δγ=arctan2(r 21 r 11 );

[0070] In the formula, r ij Δ represents the element in the i-th row and j-th column of the deviation matrix ΔR; Δα, Δβ, and Δγ represent the deviation values ​​of pitch angle, yaw angle, and roll angle, respectively.

[0071] These angular deviation parameters are automatically calculated through matrix operations, and their accuracy depends on the precision of image processing and 3D reconstruction, typically controlled within 0.005°. Using Euler angles to represent rotation is intuitive and easy to understand, but gimbal locking may occur under certain special orientations, thus requiring additional processing mechanisms in practical applications.

[0072] In step S02, the specific expression of the least squares method for calculating the centerline equation is as follows:

[0073] For the centerline equation of a long-axis part:

[0074] x = x0 + at;

[0075] y = y0 + bt;

[0076] z = z0 + ct;

[0077] In the formula, (x0, y0, z0) are the coordinates of a point on the line; (a, b, c) are the direction vectors of the line, and satisfy a 2 +b 2 +c 2 =1; t is a parameter variable.

[0078] Suppose there are n feature points (x i y i , z i For each i = 1, 2, ..., n, the objective function of the least squares method is:

[0079]

[0080] In the formula, d i For point (x) i y i , z i The distance from the line is calculated using the following formula:

[0081]

[0082] To simplify the calculation, the centroid (x) of the feature point can be used. c y c , z c As a point on the straight line, that is:

[0083]

[0084] Then construct the scatter matrix:

[0085]

[0086] The direction vector (a, b, c) of the line is the eigenvector corresponding to the largest eigenvalue of matrix M.

[0087] The axial and radial deformation matrices are constructed as follows:

[0088] Axial change matrix:

[0089]

[0090] In the formula, Δz j This represents the position coordinates of the j-th feature point on the axis along the axial direction; v zj This indicates the amount of axial displacement that needs to be adjusted at this point; m is the number of feature points, which is usually taken as m≥5.

[0091] Radial change matrix:

[0092]

[0093] In the formula, Δx j and Δy j This represents the radial coordinates of the j-th feature point on the axis; v xj and v yj This indicates the radial displacement that needs to be adjusted at this point.

[0094] The calculation of positional deviation data and angular deviation data is specifically expressed as follows:

[0095] Position deviation vector:

[0096]

[0097] In the formula, (x bearing y bearing , z bearing (x) represents the coordinates of the intersection point of the bearing centerline and the reference plane; shaft y shaft , z shaft ) represents the coordinates of the intersection point of the centerline of the long shaft part and the same reference plane.

[0098] Angular deviation vector:

[0099]

[0100] In the formula, Δθ x , Δθ y , Δθ z These represent the angles between the axis of the long shaft component and the axis of the bearing in the x, y, and z directions, respectively.

[0101] The calculation formula is:

[0102]

[0103] In the formula, and These are the axial direction vectors for the long shaft parts and the bearings, respectively. These are the unit vectors of the coordinate system.

[0104] In step S03, the calculation of the centering adjustment vector set is specifically represented as follows:

[0105]

[0106] Each adjustment vector It is a six-dimensional vector:

[0107]

[0108] In the formula, Δx i Δy i Δz i Δθ represents the displacement in the x, y, and z directions in the i-th step adjustment, respectively. xi , Δθ yi , Δθ zi These represent the rotation angles around the x, y, and z axes adjusted in the i-th step, respectively.

[0109] The formula for calculating the adjustment vector using the gradient descent algorithm is as follows:

[0110]

[0111] In the formula, This is the adjustment vector for the (i+1)th iteration; Let be the adjustment vector for the i-th iteration; η is the learning rate, which typically ranges from [0.01, 0.1]. For the objective function J in The gradient at that point.

[0112] The objective function J is defined as the weighted sum of positional and angular deviations:

[0113]

[0114] In the formula, λ p and λ a These are the weighting coefficients for positional deviation and angular deviation, respectively, typically ranging from [0.4, 0.6]; ΔP and ΔΘ are the positional deviation vector and angular deviation vector, respectively. and These are the position and angle components in the adjustment vector, respectively.

[0115] The iteration termination condition is:

[0116] or

[0117] In the formula, ε is the convergence threshold for displacement and angle, which is usually taken as 10. -6 δ is the threshold of the objective function, typically set to 10. -4 .

[0118] In step S04, the construction of the real-time centering matching matrix is ​​specifically represented as follows:

[0119]

[0120] In the formula, r ijThe resulting 3×3 submatrix is ​​a rotation matrix R, describing the orientation of the long shaft component relative to the bearing; (t x , t y , t z The vector formed by ) is a translation vector. Describe the positional offset of the long shaft component relative to the bearing.

[0121] The specific steps for calculating the real-time alignment matching matrix based on ranging sensor data are as follows:

[0122] Assume there are three laser rangefinders, whose positions in the bearing coordinate system are respectively and The measured distances are d1, d2, and d3, respectively.

[0123] First, calculate the coordinates of the corresponding points on the long shaft part:

[0124]

[0125] In the formula, Let be the unit vector of the measurement direction of the i-th sensor.

[0126] Then, using these three pairs of corresponding points, the optimal rigid body transformation matrix can be solved:

[0127]

[0128] To improve calculation accuracy, the Kalman filter algorithm is used to process the ranging data:

[0129] State prediction equation:

[0130]

[0131] Measurement update equation:

[0132]

[0133] Kalman gain calculation:

[0134]

[0135] Prior covariance update:

[0136]

[0137] Posterior covariance update:

[0138]

[0139] In the formula, For the k-th step, F is the state estimate; F is the state transition matrix; B is the control input matrix; u kFor control input; z k H represents the measured value; H is the measurement matrix; K represents the measured value. k P is the Kalman gain; k Let be the state covariance matrix; Q be the process noise covariance; and R be the measurement noise covariance.

[0140] In ranging applications, the state vector is typically the ranging value and its rate of change, i.e. The state transition matrix F and the measurement matrix H are respectively:

[0141]

[0142] In the formula, Δt is the sampling time interval, which is usually 10. -3 Second.

[0143] In step S05, the specific representation of the weighted undirected graph minimum spanning tree problem is as follows:

[0144] Graph G = (V, E), where V is the set of nodes representing different adjustment states; E is the set of edges representing adjustment operations from one state to another.

[0145] The formula for calculating the weight of an edge is:

[0146] w(e ij )=α·T ij +β·E ij +γ·D ij ;

[0147] In the formula, w(e ij ) is edge e ij The weights of T; ij E represents the time consumed in transitioning from state i to state j. ij D represents the energy consumed in transitioning from state i to state j. ij Let be the difficulty coefficient from state i to state j; α, β, and γ are the corresponding weight coefficients, with values ​​ranging from [0.4, 0.5], [0.3, 0.4], and [0.1, 0.3], respectively, and satisfying α+β+γ=1.

[0148] Time consumption T ij The calculation formula is:

[0149]

[0150] In the formula, and Let v be the six-dimensional vector representations of states i and j, respectively; max This represents the maximum speed of the attitude adjustment platform, expressed in mm / s or ° / s.

[0151] Energy consumption E ijThe calculation formula is:

[0152]

[0153] In the formula, k E This is the energy consumption coefficient, typically ranging from [0.01, 0.1], with units of J / (mm). 2 ) or J / (° 2 ).

[0154] Difficulty level D ij The calculation formula is:

[0155]

[0156] In the formula, k D λ is the difficulty baseline coefficient, typically set to [0.5, 2]; λ is the attenuation coefficient, typically set to [0.1, 1]; d min The minimum distance between the device and the obstacle or restricted area during the transition from state i to state j, in mm.

[0157] The specific steps of Kruskal's algorithm for finding the minimum spanning tree are as follows:

[0158] 1. Sort all edges by weight in ascending order;

[0159] 2. Initialize an empty spanning tree T;

[0160] 3. Traverse all edges in ascending order of weight. For the current edge e... ij :

[0161] a. If e ij Adding T will not form a cycle, so e will be... ij Add T;

[0162] b. Otherwise, discard e. ij ;

[0163] 4. Repeat step 3 until T contains |V|-1 edges.

[0164] The construction of the optimal centering position matrix is ​​specifically represented as follows:

[0165]

[0166] In the formula, r ij The 3×3 submatrix formed is the relative attitude matrix when the long shaft part and the bearing reach the optimal alignment state; (t x , t y , t z The vector formed by these vectors represents the relative position vectors of the long shaft parts and the bearings when they reach optimal alignment.

[0167] In step S06, the specific expression of the physical and mechanical equations for bearing press fitting is as follows:

[0168] The basic equation for calculating pressing force:

[0169]

[0170] In the formula, F is the pressing force, in N; μ is the contact surface friction coefficient, dimensionless, typically ranging from [0.05, 0.25]; E is the equivalent elastic modulus, in MPa, calculated using the following formula: Where E b E represents the elastic modulus of the bearing material. s δ is the elastic modulus of the shaft material; L is the contact surface length in mm; δ is the radial interference in mm, calculated using the following formula: D b This refers to the bearing's inner diameter, in mm; d s D is the outer diameter of the shaft, in mm. o This refers to the outer diameter of the bearing, in mm.

[0171] Corrected equation considering temperature factors:

[0172] δ T =δ-(D b ·α b -d s ·α s )·ΔT;

[0173] In the formula, δ T Effective interference fit taking temperature into account, in mm; α b The coefficient of linear expansion of the bearing material, in Kelvin. -1 ;α s The coefficient of linear expansion of the shaft material is expressed in K. -1 ΔT is the difference between the actual temperature and the standard temperature, in K.

[0174] Formula for calculating the optimal pressing force during the pressing process:

[0175] F opt (z)=F0+k·z+c·z 2 ;

[0176] In the formula, F opt (z) represents the optimal pressing force at a pressing depth of z, in N; F0 represents the initial contact force, in N, typically taken as [50, 200]; k is the linear stiffness coefficient, in N / mm, with a value range related to the bearing size; c is the quadratic coefficient, in N / mm. 2, is used to describe nonlinear characteristics, and its value range is usually [0.01, 0.5]; z is the pressing depth, in mm.

[0177] The piecewise function expression of the press-fit speed curve:

[0178]

[0179] In the formula, v(z) is the pressing speed when the pressing depth is z, in mm / s; v1 is the speed of the initial contact stage, which is 0.5 mm / s; v2 is the speed of the main pressing stage, which is 1 mm / s; v3 is the speed of the final positioning stage, which is 0.2 mm / s; z1 is the boundary between the initial contact stage and the main pressing stage, which is usually 10% of the bearing width; z2 is the boundary between the main pressing stage and the final positioning stage, which is usually 90% of the bearing width; L is the total width of the bearing, in mm.

[0180] In step S07, the assembly quality evaluation function is specifically represented as follows:

[0181] Q=w1·S+w2·P+w3·G-w4·A;

[0182] In the formula, Q is the assembly quality score, with a full score of 100; S is the force-displacement curve shape similarity, with a value range of [0, 1]; P is the key feature point deviation score, with a value range of [0, 1]; G is the curve slope change score, with a value range of [0, 1]; A is the anomaly coefficient, with a value range of [0, 1]; w1, w2, w3, and w4 are the corresponding weight coefficients, with a value range of [0.1, 0.5], and satisfying w1+w2+w3+w4=1.

[0183] The formula for calculating the force-displacement curve morphological similarity S is:

[0184]

[0185] In the formula, F i For the actual pressing process, in the displacement z i The pressing force measured at the point; F std (z i The standard force-displacement curve is shown at displacement z. i The pressing force at the point; n is the number of sampling points; F max This represents the maximum force value on the standard force-displacement curve.

[0186] The formula for calculating the key feature point deviation score P is:

[0187]

[0188] In the formula, F jF represents the force value at the j-th critical feature point during the actual pressing process. std，j is the force value at the j-th critical feature point in the standard force-displacement curve; m is the number of critical feature points, usually taken as 3 to 5.

[0189] The formula for calculating the score G for the change in curve slope is:

[0190]

[0191] In the formula, k is the slope of the actual force-displacement curve in the i-th segment; std，i Let be the slope of the standard force-displacement curve in the i-th segment.

[0192] The formula for calculating the anomaly coefficient A is:

[0193]

[0194] In the formula, N abn N represents the number of outliers detected. threshold This is the threshold for the number of outliers, typically set to 5% of the total number of sampling points.

[0195] The specific construction of the assembly process quality assessment matrix is ​​as follows:

[0196]

[0197] In the formula, z i F represents the displacement value of the i-th sampling point; i Let k be the force value at the i-th sampling point; i D is the slope of the force-displacement curve at the i-th sampling point; i The deviation value at the i-th sampling point is calculated using the formula D. i =|F i -F std (z i )|;A i This is an anomaly marker at the i-th sampling point. If this point is an anomaly, then A... i =1, otherwise A i =0.

[0198] The criteria for determining outliers are:

[0199] |F i -F std (z i )|>σ·F std (z i );

[0200] In the formula, σ is the abnormal threshold coefficient, which is usually taken as [0.05, 0.15].

[0201] In step S08, the calculation of the concentricity error data is specifically represented as follows:

[0202] Formula for calculating radial concentricity error:

[0203]

[0204] In the formula, ε r Radial concentricity error, in μm; (x shaft y shaft (x) represents the coordinates of the intersection point between the centerline of the assembled long shaft part and the measuring plane; bearing y bearing () represents the coordinates of the intersection point between the bearing centerline after assembly and the same measuring plane.

[0205] Formula for calculating angular concentricity error:

[0206]

[0207] In the formula, ε a This represents the concentricity error of the angle, in degrees. and These are the axial direction vectors of the assembled long shaft parts and bearings, respectively.

[0208] The formula for calculating the comprehensive evaluation index of assembly quality is:

[0209]

[0210] In the formula, I is the comprehensive evaluation index of assembly quality, with a full score of 100 points; Q is the assembly quality score calculated in step S07; ε r For radial concentricity error; ε r，max The maximum allowable radial concentricity error is 2μm for precision bearings and 5μm for ordinary bearings; ε a For angular concentricity error; ε a，max This represents the maximum permissible error for angular concentricity, typically taken as 0.01°; w Q w εr w εa These are the corresponding weight coefficients, each ranging from [0.2, 0.5], and satisfying w Q +w εr +w εa =1.

[0211] The formulas and calculation processes described above constitute the mathematical foundation of the automatic alignment and assembly method for bearings of long shaft parts. These mathematical models encompass knowledge from multiple fields, including image processing and 3D reconstruction, least squares fitting, optimization algorithms, and elasticity theory, forming a complete theoretical system.

[0212] Euler angle matrices are represented using rotation matrices because rotation matrices intuitively describe the attitude of a rigid body in three-dimensional space, facilitating coordinate transformation calculations. Choosing pitch, yaw, and roll as the three degrees of freedom parameters is a commonly used representation method in aerospace, offering the advantage of clear physical meaning.

[0213] The least squares method is used to fit the centerline equation because, in practical applications, due to measurement and manufacturing errors, the extracted feature points cannot be completely collinear. The least squares method can find the best-fitting straight line that minimizes the sum of the squares of the distances from the feature points to the line, thus obtaining the most reliable centerline equation.

[0214] The purpose of establishing a model for the minimum spanning tree problem in a weighted undirected graph is to abstract the centering adjustment process into a path optimization problem. By minimizing the time consumption, energy consumption, and operational difficulty of the adjustment process, the most economical and efficient adjustment path can be found. Kruskal's algorithm is a classic algorithm for solving the minimum spanning tree problem, characterized by its simplicity and high computational efficiency.

[0215] The physical and mechanical equations for bearing press-fitting are based on the theory of elasticity, taking into account factors such as material elastic deformation, contact friction, and thermal expansion effects, and can accurately predict the mechanical behavior during the press-fitting process. A piecewise function is used to describe the press-fitting speed curve, allowing for different control strategies at different stages of the press-fitting process, ensuring both press-fitting quality and improving assembly efficiency.

[0216] The assembly quality assessment function comprehensively considers various characteristics of the force-displacement curve, including morphological similarity, deviation of key feature points, curve slope changes, and anomalies, enabling a comprehensive evaluation of assembly quality. In particular, the use of an anomaly coefficient as a penalty term effectively identifies and marks anomalies during the assembly process, improving the accuracy and reliability of the assessment.

[0217] Compared with existing technologies, this mathematical model has the following main innovations and advantages:

[0218] First, Euler angle matrices are introduced to describe the relative attitude of long shaft parts and bearings. Compared with the traditional single-parameter description method, this method can more comprehensively characterize the position and attitude relationship in three-dimensional space and improve the alignment accuracy.

[0219] Secondly, the centering process is modeled as a weighted undirected graph minimum spanning tree problem, and the Kruskal algorithm is applied to solve the optimal adjustment path. Compared with the traditional empirical adjustment method, it can find the globally optimal adjustment strategy, thus improving the centering efficiency and stability.

[0220] Third, the physical and mechanical equations for bearing press fitting take into account a variety of influencing factors such as material properties, contact conditions, and environmental factors. Compared with simplified models, it can more accurately predict the mechanical behavior during the press fitting process and avoid the occurrence of press fitting defects.

[0221] Fourth, the assembly quality evaluation function comprehensively evaluates assembly quality from multiple dimensions. Compared with single-index evaluation methods, it can more comprehensively reflect the assembly status and improve the reliability of quality control.

[0222] Specifically, the principle of this invention is based on the interdisciplinary integration of spatial geometry, computer vision, computational mechanics, and graph theory optimization. Its working principle can be explained from four core aspects:

[0223] First, at the position perception level, this invention employs a binocular camera and a high-precision laser rangefinder to construct a multi-dimensional spatial coordinate measurement system. The binocular camera acquires the initial spatial position of the long-axis parts and bearings through triangulation, establishing an Euler angle matrix to describe their spatial attitude during the alignment process, while the high-precision laser rangefinder provides real-time distance feedback at the micrometer level. This dual-sensor system overcomes the limitations of a single measurement method, ensuring the comprehensiveness and accuracy of spatial position measurement.

[0224] Secondly, at the data processing level, this invention uses the least squares method to process image data, calculates the centerline equations of the long-axis parts and bearings, and then constructs axial and radial change matrices. This method can effectively filter out random measurement errors and improve the accuracy of centerline calculation. Simultaneously, the centering process is modeled as a weighted undirected graph minimum spanning tree problem, and the optimal adjustment path is solved using the Kruskal algorithm. This mathematical optimization method ensures the minimum cost and maximum efficiency of the adjustment process.

[0225] Furthermore, at the execution and control level, this invention, based on the physical and mechanical equations of bearing press-fitting, considers physical parameters such as the material's elastic modulus and coefficient of friction to accurately calculate the optimal press-fitting parameters. This parameter calculation method based on a physical model ensures that the press-fitting process conforms to the laws of material mechanics, avoiding assembly defects that may result from blindly operating based on experience. The multi-degree-of-freedom precision attitude adjustment platform then performs precise adjustments based on the calculation results, achieving sub-micron level alignment accuracy.

[0226] Finally, at the quality assessment level, this invention innovatively constructs an assembly process quality assessment matrix. By comparing and analyzing real-time data collected by force and displacement sensors with standard force-displacement curve parameters, and considering environmental temperature factors, a quantitative assessment of assembly quality is achieved. This data-driven quality assessment method breaks through the limitations of traditional experience-based judgment and provides objective and quantifiable quality assurance.

[0227] The reason why the technical solution of the present invention can effectively solve the technical problem of precise alignment and assembly of long shaft parts and bearings is that it establishes a complete closed-loop system of measurement-calculation-execution-evaluation, with smooth information flow between each link, realizing intelligent and precise control of the assembly process. At the same time, it fully considers the physical properties of materials and environmental factors, so that the assembly process meets both theoretical expectations and adapts to actual working conditions.

[0228] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0229] The specific implementation of step S01 involves acquiring multi-angle images of the long shaft part and bearing using an industrial-grade binocular camera. The acquisition frequency is set to 25 frames per second to ensure real-time dynamic image data. The binocular camera employs stereo vision principles, simultaneously imaging the same scene using two cameras at different positions, and calculating the three-dimensional spatial information of the target object using the parallax principle. During image acquisition, the camera resolution is set to 1920×1080 pixels, and an adaptive exposure algorithm is used to ensure image clarity. After preprocessing, the contour features of the long shaft part and bearing are extracted from the acquired raw images. Based on the extracted feature point coordinate data, the Euler angle matrix for the alignment process is calculated, specifically represented as:

[0230] R = R z (γ)·R y (β)·R x (α);

[0231] In the formula, R is the Euler angle matrix for the centering process; R x (α) is the rotation matrix for rotating about the x-axis by an angle α (pitch angle); R y (β) is the rotation matrix for rotating about the y-axis by an angle β (yaw angle); R z (γ) is the rotation matrix for rotating about the z-axis by an angle γ (roll angle).

[0232] The matrix expansion is as follows:

[0233]

[0234] The centering deviation Euler angle matrix is ​​calculated by comparing the actual Euler angles with the target Euler angles under ideal assembly conditions. The calculation formula is as follows:

[0235]

[0236] In the formula, ΔR is the Euler angle matrix of the centering deviation; R target R is the Euler angle matrix in the target assembly state; actual This is the Euler angle matrix as measured in practice; For R target The inverse matrix.

[0237] The formula for extracting the deviation angle from the centering deviation Euler angle matrix is ​​as follows:

[0238] Δα=arctan2(r 32 r 33 ); Δβ=arcsin(-r 31 ); Δγ=arctan2(r 21 r 11 );

[0239] In the formula, r ij This represents the element in the i-th row and j-th column of the deviation matrix ΔR; Δα, Δβ, and Δγ represent the deviation values ​​of pitch angle, yaw angle, and roll angle, respectively, with angular accuracy controlled within 0.01°. The purpose of this step is to establish an accurate mathematical model of the initial position of the long shaft component and the bearing, providing basic data support for the subsequent alignment process.

[0240] The specific implementation of step S02 is based on the image acquisition data obtained in step S01. First, image segmentation processing is performed to separate the long shaft part and bearing area from the background. An edge detection algorithm is used to extract feature point sets of the outer contour line of the long shaft part and the inner contour line of the bearing, with no less than 50 feature points extracted for each contour. A least squares fitting algorithm is applied to these feature points to construct the centerline equation of the long shaft part and the bearing, specifically expressed as:

[0241] x=x0+at; y=y0+bt; z=z0+ct;

[0242] In the formula, (x0, y0, z0) are the coordinates of a point on the line; (a, b, c) are the direction vectors of the line, and satisfy a 2 +b 2 +c 2 =1; t is a parameter variable.

[0243] Suppose there are n feature points (x i y i , z i For each i = 1, 2, ..., n, the objective function of the least squares method is:

[0244]

[0245] In the formula, d i For point (x) i y i , z i The distance from the line is calculated using the following formula:

[0246]

[0247] To simplify the calculation, the centroid (x) of the feature points is... c y c , z c As a point on the straight line, construct the scatter matrix:

[0248]

[0249] The direction vector (a, b, c) of the straight line is the eigenvector corresponding to the largest eigenvalue of matrix M. By comparing the relative positions of the centerlines of the long shaft parts and the bearing centerlines, axial and radial deformation matrices are constructed.

[0250] Axial change matrix:

[0251]

[0252] In the formula, Δz j This represents the position coordinates of the j-th feature point on the axis along the axial direction; v zj This indicates the amount of axial displacement that needs to be adjusted at this point; m is the number of feature points, which is usually taken as m≥5.

[0253] Radial change matrix:

[0254]

[0255] In the formula, Δx j and Δy j This represents the radial coordinates of the j-th feature point on the axis; v xj and v yj This indicates the radial displacement that needs to be adjusted at this point.

[0256] The position deviation vector and the angle deviation vector are calculated as follows:

[0257]

[0258] Formula for calculating angular deviation:

[0259]

[0260] In the formula, and These are the axial direction vectors for the long shaft parts and the bearings, respectively. These are the unit vectors of the coordinate system. The purpose of this step is to accurately quantify the positional and angular deviations between the long shaft parts and the bearings, providing precise data for subsequent alignment adjustments.

[0261] The specific implementation of step S03 involves generating an alignment adjustment vector set based on the positional and angular deviation data calculated in step S02, combined with preset accuracy requirements. The preset accuracy requirements include a radial deviation limit of no more than 5 μm, an axial deviation limit of no more than 10 μm, and an angular deviation limit of no more than 0.005°. The mathematical representation of the alignment adjustment vector set is as follows:

[0262]

[0263] Each adjustment vector It is a six-dimensional vector:

[0264]

[0265] In the formula, Δx i Δy i Δz i Δθ represents the displacement in the x, y, and z directions in the i-th step adjustment, respectively. xi , Δθ yi , Δθ zi These represent the rotation angles around the x, y, and z axes adjusted in the i-th step, respectively.

[0266] The vector set is generated using the gradient descent algorithm, and the calculation formula is as follows:

[0267]

[0268] In the formula, This is the adjustment vector for the (i+1)th iteration; Let be the adjustment vector for the i-th iteration; η is the learning rate, which typically ranges from [0.01, 0.1]. For the objective function J in The gradient at that point.

[0269] The objective function J is defined as the weighted sum of positional and angular deviations:

[0270]

[0271] In the formula, λ p and λ a These are the weighting coefficients for positional deviation and angular deviation, respectively, typically ranging from [0.4, 0.6]; ΔP and ΔΘ are the positional deviation vector and angular deviation vector, respectively. and These are the position and angle components in the adjustment vector, respectively. Based on the data from the centering adjustment vector set, the system controls a multi-degree-of-freedom precision attitude adjustment platform to perform preliminary position adjustments. This platform employs a six-axis parallel mechanism design, possessing three translational degrees of freedom and three rotational degrees of freedom, achieving a positioning accuracy of 0.1 μm and an angle adjustment accuracy of 0.001°. The purpose of this step is to adjust the long-axis components and bearings to a pre-alignment state that meets the preset accuracy requirements, creating conditions for subsequent precise alignment operations.

[0272] The specific implementation of step S04 involves using a six-degree-of-freedom robotic arm to control the long shaft part to slowly approach the bearing, with the movement speed set to no more than 5 mm / s. Simultaneously, at least three high-precision laser rangefinders are deployed, with a measurement accuracy of no less than 0.5 μm and a sampling frequency of no less than 1000 Hz, evenly distributed at 120° around the bearing, to monitor the relative position data between the long shaft part and the bearing in real time. A real-time alignment matching matrix is ​​constructed based on the rangefinder sensor data.

[0273]

[0274] In the formula, r ij The resulting 3×3 submatrix is ​​a rotation matrix R, describing the orientation of the long shaft component relative to the bearing; (t x , t y , t z The vector formed by ) is a translation vector. Describe the positional offset of the long shaft component relative to the bearing.

[0275] Sensor data is processed using the Kalman filter algorithm. The key equations of the Kalman filter include:

[0276] State prediction equation:

[0277] Measurement update equation:

[0278] Kalman gain calculation:

[0279] In the formula, For the k-th step, F is the state estimate; F is the state transition matrix; B is the control input matrix; u k For control input; z k H represents the measured value; H is the measurement matrix; K represents the measured value. k P is the Kalman gain; k Let be the state covariance matrix; Q be the process noise covariance; and R be the measurement noise covariance. In ranging applications, the state vector is typically the ranging value and its rate of change, i.e. The real-time alignment matrix is ​​updated at a frequency of 100Hz to ensure that the system can respond promptly to position changes. The purpose of this step is to achieve a precise approach between the long shaft component and the bearing, and to monitor the relative positional relationship in real time using high-precision sensors, providing data support for subsequent precise alignment adjustments.

[0280] The specific implementation of step S05 involves modeling the centering process as a weighted undirected graph minimum spanning tree problem based on the real-time centering matching matrix feedback data obtained in step S04. Nodes represent adjustment states, the total number of nodes is no less than 100, and the edge weights are calculated using the following formula:

[0281] w(e ij )=α·T ij +β·E ij +γ·D ij ;

[0282] In the formula, w(e ij ) is edge e ij The weights of T; ij E represents the time consumed in transitioning from state i to state j. ij D represents the energy consumed in transitioning from state i to state j. ij Let be the difficulty coefficient from state i to state j; α, β, and γ are the corresponding weight coefficients, with values ​​ranging from [0.4, 0.5], [0.3, 0.4], and [0.1, 0.3], respectively, and satisfying α+β+γ=1.

[0283] The formulas for calculating time consumption, energy consumption, and difficulty level are as follows:

[0284]

[0285] In the formula, and Let v be the six-dimensional vector representations of states i and j, respectively; max k is the maximum speed of the attitude adjustment platform. E This is the energy consumption coefficient, typically ranging from [0.01, 0.1]; k D λ is the difficulty baseline coefficient, typically set to [0.5, 2]; λ is the attenuation coefficient, typically set to [0.1, 1]; d min It is the minimum distance to the obstacle or restricted area during the process from state i to state j.

[0286] Based on the constructed weighted undirected graph, the Kruskal algorithm is applied to solve for the minimum spanning tree, obtaining the optimal adjustment path data from the initial state to the target state. The Kruskal algorithm is based on a greedy strategy, selecting edges in ascending order of weight while avoiding loops, ultimately generating a minimum weight spanning tree containing all nodes. The system controls a multi-degree-of-freedom precision attitude adjustment platform to precisely adjust along the optimal adjustment path data, ultimately achieving precise alignment of the long-axis component and the bearing, and constructing the optimal alignment position matrix.

[0287]

[0288] In the formula, r ij The 3×3 submatrix formed is the relative attitude matrix when the long shaft part and the bearing reach the optimal alignment state; (t x , t y , t z The vector formed by these steps represents the relative position vectors of the long shaft component and the bearing when they are optimally aligned. The purpose of this step is to solve for the optimal adjustment path using an optimization algorithm, achieving high-precision alignment between the long shaft component and the bearing, and creating the best initial conditions for subsequent press-fitting operations.

[0289] The specific implementation of step S06 involves calculating the optimal press-fit parameters based on the physical and mechanical equations of bearing press-fitting after achieving precise alignment. First, input parameters are read, including the bearing inner diameter, shaft outer diameter, bearing material elastic modulus, shaft material elastic modulus, and contact surface friction coefficient. The basic equation for calculating the press-fitting force is:

[0290]

[0291] In the formula, F is the pressing force, in N; μ is the contact surface friction coefficient, dimensionless, typically ranging from [0.05, 0.25]; E is the equivalent elastic modulus, in MPa, calculated using the following formula: Where E b E represents the elastic modulus of the bearing material. s δ is the elastic modulus of the shaft material; L is the contact surface length in mm; δ is the radial interference in mm, calculated using the following formula: D b This refers to the bearing's inner diameter, in mm; d s D is the outer diameter of the shaft, in mm. o This refers to the outer diameter of the bearing, in mm.

[0292] Corrected equation considering temperature factors:

[0293] δ T =δ-(D b ·α b -ds ·α s )·ΔT;

[0294] In the formula, δ T Effective interference fit taking temperature into account, in mm; α b The coefficient of linear expansion of the bearing material, in Kelvin. -1 ;α s The coefficient of linear expansion of the shaft material is expressed in K. -1 ΔT is the difference between the actual temperature and the standard temperature, in K.

[0295] Formula for calculating the optimal pressing force during the pressing process:

[0296] F opt (z)=F0+k·z+c·z 2 ;

[0297] In the formula, F opt (z) represents the optimal pressing force at a pressing depth of z, in N; F0 represents the initial contact force, in N, typically taken as [50, 200]; k is the linear stiffness coefficient, in N / mm, with a value range related to the bearing size; c is the quadratic coefficient, in N / mm. 2 , is used to describe nonlinear characteristics, and its value range is usually [0.01, 0.5]; z is the pressing depth, in mm.

[0298] The press-fit speed curve adopts a segmented control strategy, and the expression is:

[0299]

[0300] In the formula, v(z) is the pressing speed at a pressing depth of z, in mm / s; v1 is the initial contact stage speed, taken as 0.5 mm / s; v2 is the main pressing stage speed, taken as 1 mm / s; v3 is the final positioning stage speed, taken as 0.2 mm / s; z1 is the boundary between the initial contact stage and the main pressing stage, usually taken as 10% of the bearing width; z2 is the boundary between the main pressing stage and the final positioning stage, usually taken as 90% of the bearing width; L is the total width of the bearing, in mm. The system controls the hydraulic pressing mechanism based on the calculation results to smoothly press the bearing onto the long shaft part along the axial direction. The purpose of this step is to calculate the optimal pressing parameters based on physical and mechanical principles to ensure a smooth and controllable bearing pressing process and avoid pressing defects.

[0301] The specific implementation of step S07 involves continuously monitoring assembly force and displacement data during the press-fitting process using force and displacement sensors. The force sensor employs a piezoelectric design, with a measurement range of 0–50 kN, an accuracy of no less than 0.1%, and a sampling frequency of no less than 1000 Hz. The displacement sensor employs a capacitive design, with a measurement range of 0–50 mm, an accuracy of no less than 0.1 μm, and a sampling frequency of no less than 1000 Hz. The system collects sensor data in real time, constructs a real-time dataset of assembly force and displacement data, and analyzes the data using an assembly quality evaluation function based on this real-time dataset.

[0302] Q=w1·S+w2·P+w3·G-w4·A;

[0303] In the formula, Q is the assembly quality score, with a full score of 100; S is the force-displacement curve shape similarity, with a value range of [0, 1]; P is the key feature point deviation score, with a value range of [0, 1]; G is the curve slope change score, with a value range of [0, 1]; A is the anomaly coefficient, with a value range of [0, 1]; w1, w2, w3, and w4 are the corresponding weight coefficients, with a value range of [0.1, 0.5], and satisfying w1+w2+w3+w4=1.

[0304] The calculation formulas for each evaluation indicator are as follows:

[0305]

[0306] In the formula, F i For the actual pressing process, in the displacement z i The pressing force measured at the point; F std (z i The standard force-displacement curve is shown at displacement z. i The pressing force at the point; n is the number of sampling points; F max The maximum force value on the standard force-displacement curve; F j F represents the force value at the j-th critical feature point during the actual pressing process. std，j is the force value at the j-th critical feature point in the standard force-displacement curve; m is the number of critical feature points, usually taken as 3 to 5. k is the slope of the actual force-displacement curve in the i-th segment; std，i N represents the slope of the standard force-displacement curve in the i-th segment. abn N represents the number of outliers detected. threshold This is the threshold for the number of outliers, typically set to 5% of the total number of sampling points.

[0307] The system constructs an assembly process quality assessment matrix based on the evaluation results:

[0308]

[0309] In the formula, z i F represents the displacement value of the i-th sampling point; i Let k be the force value at the i-th sampling point; i D is the slope of the force-displacement curve at the i-th sampling point; i The deviation value at the i-th sampling point is calculated using the formula D. i =|F i -F std (z i )|;A i This is an anomaly marker at the i-th sampling point. If this point is an anomaly, then A... i =1, otherwise A i =0.

[0310] The criteria for determining outliers are:

[0311] |F i -F std (z i )|>σ·F std (z i );

[0312] In the formula, σ is the anomaly threshold coefficient, typically set to [0.05, 0.15]. Assembly quality is scored on a 100-point scale: 90 points or above is excellent, 75-90 points is acceptable, and below 75 points is unacceptable. The purpose of this step is to monitor key parameters during the pressing process in real time, promptly identify anomalies, and ensure assembly quality.

[0313] The specific implementation of step S08 involves restarting the binocular camera after assembly to inspect the assembly result. The camera acquires images of the assembled long shaft parts and bearings at the same resolution as in step S01 to ensure inspection accuracy. The system processes the acquired images, extracts the contour features of the long shaft parts and bearings, and calculates the concentricity error data after assembly. The concentricity calculation uses the least squares method to fit the center coordinates of the circle, and then calculates the deviation value between the center lines of the shaft and the bearing. The calculation formulas for radial concentricity error and angular concentricity error are as follows:

[0314]

[0315] In the formula, ε r Radial concentricity error, in μm; (x shaft y shaft (x) represents the coordinates of the intersection point between the centerline of the assembled long shaft part and the measuring plane; bearing y bearing ) represents the coordinates of the intersection point between the bearing centerline after assembly and the same measuring plane; ε a This represents the concentricity error of the angle, in degrees. and These are the axial direction vectors of the assembled long shaft parts and bearings, respectively.

[0316] The system determines whether the concentricity error data meets the assembly accuracy requirements. These requirements are determined based on the bearing dimensions. For precision bearings, the concentricity error should not exceed 2μm; for ordinary bearings, the concentricity error should be controlled within 5μm. The system combines assembly quality scoring data, abnormal condition judgment results, and concentricity error data to generate a comprehensive assembly quality evaluation index.

[0317]

[0318] In the formula, I is the comprehensive evaluation index of assembly quality, with a full score of 100 points; Q is the assembly quality score calculated in step S07; ε r For radial concentricity error; ε r，max The maximum allowable radial concentricity error is 2μm for precision bearings and 5μm for ordinary bearings; ε a For angular concentricity error; ε a，max This represents the maximum permissible error for angular concentricity, typically taken as 0.01°; w Q w εr w εa These are the corresponding weight coefficients, each ranging from [0.2, 0.5], and satisfying w Q +w εr +w εa =1. The purpose of this step is to conduct a final inspection of the assembly results, confirm whether the assembly quality meets the requirements, and generate a complete quality assessment report to provide a basis for continuous improvement of the assembly process.

[0319] The steps S01 to S08 described above constitute the complete implementation process of the automatic alignment and assembly method for bearings of long shaft parts. This method introduces mathematical models such as the Euler angle matrix for the alignment process, the Euler angle matrix for the alignment deviation, the axial change matrix, and the radial change matrix. Combined with calculation methods such as least squares, gradient descent, Kalman filtering, and Kruskal's minimum spanning tree algorithm, it achieves high-precision control of the assembly process. Simultaneously, by establishing the physical and mechanical equations for bearing press-fitting and the assembly quality evaluation function, it ensures the reliability of the assembly process and the high quality of the assembly results.

[0320] This method innovatively represents the centering process as an Euler angle matrix transformation, improving the accuracy of the description; it models the adjustment process as a weighted undirected graph minimum spanning tree problem, optimizing the adjustment path; and it introduces an assembly quality evaluation function that comprehensively considers multiple factors, enhancing the comprehensiveness of quality control. Compared with traditional assembly methods, this method significantly improves assembly accuracy, assembly efficiency, and quality stability.

[0321] In practical applications, this method is suitable for assembling bearings on various long-shaft parts, such as automotive drive shafts, industrial equipment spindles, and wind turbine shafts. Depending on the characteristics of different assembly objects, the range of relevant parameters can be adjusted, such as preset accuracy requirements, pressing force, and pressing speed. Key equipment used in the implementation process includes a binocular camera, a multi-degree-of-freedom precision attitude adjustment platform, a high-precision laser rangefinder, a six-degree-of-freedom robotic arm, and a hydraulic pressing mechanism. The accuracy of the equipment directly affects the quality of the assembly results.

[0322] To better understand and implement this invention, a specific application scenario is provided below as Example 2: Researchers applied this automated bearing alignment and assembly method during the manufacturing process of a key component of an aero-engine, automating the assembly of the turbine shaft and precision bearing. The turbine shaft is 375mm long, 42mm in diameter, and made of GH4169 high-temperature alloy with an elastic modulus of 2.10 × 10⁻⁶. 5 MPa; The assembled bearing is a precision angular contact ball bearing with an inner diameter of 42.015 mm, an outer diameter of 78 mm, a material of GCr15, and an elastic modulus of 2.15 × 10⁻⁶ MPa. 5 MPa. The assembly process employed equipment such as a binocular camera (1920×1080 pixels resolution), a six-axis parallel precision attitude adjustment platform (positioning accuracy 0.1μm, angle accuracy 0.001°), a high-precision laser rangefinder (accuracy 0.5μm, sampling frequency 1000Hz), and a hydraulic pressing mechanism (pressure control accuracy 0.5%).

[0323] First, real-time images of the turbine shaft and bearing are acquired using a binocular camera at a rate of 25 frames per second. Contour feature points are extracted through image processing, and the Euler angle matrix of the turbine shaft and bearing is calculated. In actual measurements, the Euler angle parameter of the turbine shaft is α. shaft =0.032°, β shaft = -0.021°, γ shaft =0.015°, the Euler angle parameter of the bearing is α bearing = -0.005°, β bearing =0.011°, γ bearing = -0.008°. Based on these parameters, the components of the centering deviation Euler angle matrix are shown in Table 1:

[0324] Table 1 Components of the Euler angle matrix for centering deviation

[0325] Matrix elements numerical values <![CDATA[r 11 ]]> 0.99997 <![CDATA[r 12 ]]> -0.00023 <![CDATA[r 13 ]]> 0.00032 <![CDATA[r 21 ]]> 0.00026 <![CDATA[r 22 ]]> 0.99999 <![CDATA[r 23 ]]> -0.00037 <![CDATA[r 31 ]]> -0.00035 <![CDATA[r 32 ]]> 0.00041 <![CDATA[r 33 ]]> 0.99998

[0326] Based on image acquisition data, the centerline equations of the turbine shaft and bearing were calculated using the least squares method. For the turbine shaft, 78 feature points were extracted, and the calculated centerline equation parameters were x0 = 156.827 mm, y0 = 245.132 mm, z0 = 512.075 mm, with direction vectors a = 0.001258, b = -0.000873, and c = 0.999999. For the bearing, 62 feature points were extracted, and the calculated centerline equation parameters were x0 = 156.793 mm, y0 = 245.156 mm, z0 = 512.075 mm, with direction vectors a = 0.001027, b = -0.000621, and c = 0.999999. By comparing the relative positional relationship between the turbine shaft and bearing centerlines, axial and radial change matrices were constructed, and the calculated positional and angular deviation data are shown in Table 2.

[0327] Table 2. Positional and angular deviation data

[0328] Deviation type X direction Y direction Z direction Position deviation (μm) 34.2 -24.5 0.0 Angle deviation(°) 0.037 -0.032 0.023

[0329] Based on the positional and angular deviation data, and combined with the preset accuracy requirements (radial deviation limit 3μm, axial deviation limit 5μm, angular deviation limit 0.003°), a gradient descent algorithm is used to generate a centering adjustment vector set. The algorithm parameters are set as follows: learning rate η = 0.05, positional deviation weight coefficient λ... p =0.55, angular deviation weighting coefficient λ a =0.45, the iteration termination condition is ε = 5 × 10 -7 δ=8×10 -5 After 17 iterations, the optimal adjustment vector was obtained, as shown in Table 3:

[0330] Table 3 Centering Adjustment Vector Data

[0331] Adjust components Adjustment value Displacement in the X direction (μm) -33.7 Y-direction displacement (μm) 24.3 Z-direction displacement (μm) 0.0 Rotate about the X-axis (°) -0.036 Rotate about the Y-axis (°) 0.031 Rotate about the Z-axis (°) -0.022

[0332] A multi-degree-of-freedom precision attitude adjustment platform performs adjustment movements to bring the turbine shaft and bearing to a pre-aligned state. Next, a six-degree-of-freedom robotic arm controls the turbine shaft to slowly approach the bearing at a speed of 3 mm / s. Simultaneously, three high-precision laser rangefinders are positioned at 120° evenly distributed around the bearing to monitor relative position data in real time. The laser rangefinder data is processed using a Kalman filter, and the state transition matrix is ​​set to... The measurement matrix is ​​set to H = (1 0), and the process noise covariance is set to... The measurement noise covariance is set to R = 0.25.

[0333] The centering process is modeled as a weighted undirected graph minimum spanning tree problem, with 120 nodes and edge weights calculated using parameters α = 0.45, β = 0.35, and γ = 0.2. The maximum speed v in the time consumption coefficient is... max Set to 5mm / s, energy consumption coefficient k E Set the difficulty coefficient k to 0.05. D The value is set to 1.2, and the attenuation coefficient λ is set to 0.5. The Kruskal algorithm is applied to solve for the minimum spanning tree, and the optimal adjustment path data is obtained, as shown in Table 4.

[0334] Table 4 Key Node Data for the Optimal Adjustment Path

[0335]

[0336] The multi-degree-of-freedom precision attitude adjustment platform precisely adjusts along the optimal adjustment path, ultimately achieving precise alignment between the turbine shaft and the bearing. After achieving precise alignment, the optimal pressing parameters are calculated based on the physical and mechanical equations of bearing pressing. The bearing inner diameter is 42.015 mm, the shaft outer diameter is 42.025 mm, the interference fit is 0.01 mm, the contact surface length is 25 mm, and the contact surface friction coefficient is 0.12. The calculated pressing force is 7250 N, and the pressing speed curve has three stages with speeds of 0.5 mm / s (0-2.5 mm), 1 mm / s (2.5-22.5 mm), and 0.2 mm / s (22.5-25 mm).

[0337] During the press-fitting process, force and displacement data are continuously monitored using force and displacement sensors at a sampling frequency of 1000Hz. The weighting coefficients of the assembly quality evaluation function are set to w1 = 0.4, w2 = 0.3, w3 = 0.2, w4 = 0.1, and the anomaly threshold coefficient σ is set to 0.08. The evaluation indicators calculated based on the real-time monitoring data are shown in Table 5.

[0338] Table 5 Assembly Quality Evaluation Indicators

[0339] Evaluation indicators numerical values Similarity of force-displacement curve morphology 0.968 Key feature point deviation score 0.942 Curve slope change score 0.937 Anomaly coefficient 0.021 Assembly quality rating 93.76

[0340] After assembly, the binocular camera was restarted to inspect the assembly results and calculate the concentricity error data. The radial concentricity error was 1.37 μm, and the angular concentricity error was 0.0023°, both meeting the precision requirements for precision bearing assembly (radial concentricity error not exceeding 2 μm, angular concentricity error not exceeding 0.01°). Based on the overall assembly quality score, abnormal condition judgment results, and concentricity error data, the comprehensive assembly quality evaluation index was 94.31 points, and the assembly result reached an excellent level.

[0341] Traditional turbine shaft bearing assembly methods rely primarily on manual experience or semi-automated equipment for alignment and press-fitting. Manual alignment typically depends on experienced technicians using simple tools like dial indicators and feeler gauges for measurement and adjustment, resulting in alignment accuracy usually within the 10-20 μm range. This leads to inconsistent assembly quality and low efficiency. While semi-automated assembly equipment improves efficiency, it lacks real-time monitoring and dynamic adjustment capabilities, achieving alignment accuracy generally between 5-10 μm, and is unable to effectively address changes in material properties and environmental factors. In contrast, the automatic alignment assembly method of this invention, by introducing computer vision technology, precision measurement technology, and intelligent optimization algorithms, achieves high-precision (radial concentricity error less than 2 μm) automatic alignment assembly, improving assembly efficiency (assembly time reduced by approximately 65%) and quality stability (pass rate increased to 99.2%). In particular, by modeling the alignment process as a weighted undirected graph minimum spanning tree problem and applying Kruskal's algorithm to solve for the optimal adjustment path, alignment efficiency and accuracy are significantly improved, reducing the number of adjustments by approximately 38% compared to traditional methods. Meanwhile, the introduction of assembly quality evaluation functions enables full-process quality monitoring of the assembly process, allowing for timely detection and correction of abnormal conditions and effectively preventing assembly defects. These technological innovations have significantly improved the assembly quality and efficiency of high-precision turbine shaft bearings, providing crucial support for the manufacturing of key components for aero-engines.

[0342] It should be noted that the variables involved in this invention are explained in detail in Tables 6 and 7 below.

[0343] Table 6. Variable Explanation Table (Part 1)

[0344]

[0345]

[0346] Table 7. Variable Explanation Table (Part Two)

[0347]

[0348]

[0349] Table 8. Variable Explanation Table (Part 3)

[0350]

[0351] Table 9. Variable Explanation Table (Part Four)

[0352]

[0353]

[0354] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of automatically centering a bearing for assembly on a long shaft part, comprising: Real-time image acquisition of long shaft parts and bearings is performed using a binocular camera to obtain image acquisition data and determine the deviation data between long shaft parts and bearings. Based on the deviation data, a centering adjustment vector set is generated to control the multi-degree-of-freedom precision attitude adjustment platform to perform preliminary position adjustment. A robotic arm is used to bring long shaft parts close to the bearing, while a high-precision laser rangefinder sensor monitors the relative position in real time. The alignment process is modeled as a weighted undirected graph minimum spanning tree problem. The minimum spanning tree is solved to obtain the optimal adjustment path data and achieve precise alignment. The pressing parameters are calculated based on the physical and mechanical equations of bearing pressing, and the hydraulic pressing mechanism is started to perform pressing. The step of acquiring real-time images of the long shaft parts and bearings using a binocular camera to obtain image acquisition data further includes: determining the initial position state of the long shaft parts and bearings, and constructing the Euler angle matrix for the centering process and the Euler angle matrix for the centering deviation. The centering process Euler angle matrix describes the relative attitude of the long shaft part and the bearing in three-dimensional space. It represents the spatial relationship between the two by rotation angle and includes three components: pitch angle, yaw angle and roll angle. It is used to accurately describe the relative position state of the two parts during the assembly process. The alignment deviation Euler angle matrix represents the angular difference between the ideal and actual assembly positions of the long shaft parts and bearings. It consists of angular deviations in three directions and is used to calculate the angular parameters that need to be adjusted. The real-time monitoring of relative position using a high-precision laser rangefinder further includes: constructing a real-time alignment matching matrix, which is a data matrix dynamically constructed during the assembly process that reflects the real-time relative positional relationship between the long shaft parts and the bearings. The matrix is ​​updated in real time through feedback data from the high-precision laser rangefinder to precisely control the alignment process. The precise alignment includes: constructing an optimal alignment position matrix, which describes the spatial relationship data set when the long shaft parts and bearings reach the optimal assembly position, serving as the trigger condition and benchmark for the press-fitting operation, and ensuring that press-fitting is performed under the optimal alignment state.

2. The method for automatically aligning and assembling bearings on long shaft parts according to claim 1, characterized in that, The determination of the deviation data between the long shaft component and the bearing further includes: determining the positional deviation data and the angular deviation data, and constructing the axial change matrix and the radial change matrix.

3. The method for automatically aligning and assembling bearings on long shaft parts according to claim 2, characterized in that, The axial change matrix describes the displacement adjustment required for the long shaft component along its axial direction, including the positional changes of multiple feature points on the axis, and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform axial adjustment.

4. The method for automatically aligning and assembling bearings on long shaft parts according to claim 3, characterized in that, The radial change matrix describes the displacement adjustment required for the long shaft component in the direction perpendicular to its axis, including the displacement in the horizontal and vertical directions, and is used to guide the multi-degree-of-freedom precision attitude adjustment platform to perform radial adjustment.

5. The method for automatically aligning and assembling bearings on long shaft parts according to claim 4, characterized in that, The centering adjustment vector set is a set of three-dimensional adjustment vectors calculated based on the position deviation data and the angle deviation data. It includes the adjustment direction and adjustment amount and is used to control the multi-degree-of-freedom precision attitude adjustment platform to perform precise adjustment actions.

Images