A method for wear prediction of a crane drive system

Abstract

The present application relates to the technical field of wear prediction, and particularly relates to a wear prediction method for a crane transmission system. The method comprises the following steps: acquiring tooth profile geometric parameters and material fatigue characteristics, determining meshing trajectory curves and contact point pressure distribution, acquiring contact point displacement sequences, extracting trajectory node distribution and calculating curvature distribution, determining contact point migration rate and velocity gradient distribution, judging the direction angle change rate in the velocity gradient distribution, determining the coordinates of the velocity mutation point, calculating the contact point pressure distribution at the mutation point, determining the stress concentration point position, calculating the local wear rate, acquiring the tooth surface local wear distribution data, simulating and analyzing the stress concentration point distribution of the high wear area, recalculating the optimized contact point displacement sequences and local wear distribution data, and obtaining the contact point distribution optimization result. The present application solves the deficiencies of traditional technology in wear prediction, can identify the wear trend at an early stage, and can perform maintenance and optimization in advance, thereby reducing the downtime.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wear prediction, in particular to a crane transmission system wear prediction method. BACKGROUND

[0002] As heavy machinery equipment, cranes play an important role in the material handling process in construction, port and other places. Its transmission system as the core component of the crane, bears the power transmission from the power source to the hook. Due to the long-term high load and high frequency operation of the crane, the wear problem of the gear in the transmission system gradually highlights, which directly affects the service life and operating efficiency of the crane.

[0003] In the traditional crane transmission system, the wear problem of the gear is usually discovered after the equipment fails, resulting in high cost of equipment maintenance and replacement, and increase of downtime. Therefore, how to predict the wear condition of the gear and carry out maintenance in advance through effective monitoring and early warning mechanism is a technical problem to be solved in the field of crane transmission system at present.

[0004] In the prior art, most methods use traditional monitoring methods based on vibration analysis, oil monitoring or temperature monitoring to speculate the health condition of the gear, but these methods are difficult to achieve accurate wear prediction, and have poor adaptability to the running environment and working conditions of the equipment. The traditional wear prediction technology often relies on experience judgment or simple statistical model, and lacks dynamic simulation and comprehensive analysis of the gear meshing process.

[0005] In view of this technical problem, the introduction of modern computer simulation technology and finite element analysis (FEA) method provides a new direction for gear wear prediction. Through accurate acquisition of gear design parameters, combined with material properties and finite element analysis, the wear process of the gear under actual working conditions can be more accurately simulated, the high wear area can be predicted and the gear design can be optimized, so as to effectively improve the reliability and life of the transmission system.

[0006] However, the current finite element analysis method mostly focuses on static or simple dynamic calculation, lacking fine analysis under high load working conditions, especially in complex working conditions of heavy machinery such as cranes. Therefore, an advanced prediction method considering gear geometric parameters, material properties and dynamic behavior is needed to early warn wear trend and optimize the design of crane transmission system, improve overall work efficiency and safety.

[0007] Therefore, the present application provides a crane transmission system wear prediction method, which solves the shortcomings of traditional technology in wear prediction by combining gear design, material properties and finite element analysis, can identify wear trend at an early stage, carry out maintenance and optimization in advance, thereby reducing downtime, improving equipment efficiency and economy. SUMMARY

[0008] The application provides a wear prediction method for a crane transmission system, mainly comprising:

[0009] Step S1: obtaining tooth profile geometric parameters and material fatigue characteristics from gear design parameters, determining meshing trajectory curves and contact point pressure distribution through finite element analysis, and obtaining contact point displacement sequences;

[0010] Step S2: extracting trajectory node distribution and calculating curvature distribution according to the contact point displacement sequences, and determining contact point migration rate and velocity gradient distribution based on the curvature distribution;

[0011] Step S3: judging the directional angle change rate in the velocity gradient distribution, determining the coordinates of the velocity mutation point, and calculating the contact point pressure distribution at the mutation point through the Hertz contact theory;

[0012] Step S4: determining the stress concentration point position according to the contact point pressure distribution at the mutation point, calculating the local wear rate through the wear rate calculation formula, and obtaining the tooth surface local wear distribution data;

[0013] Step S5: obtaining the high wear area according to the local wear distribution data, the contact point pressure distribution and the dynamic simulation model, and taking the high wear area as the wear prediction data, analyzing the stress concentration point distribution of the high wear area through dynamic finite element simulation, adjusting the curvature radius to generate improved tooth profile geometric parameters, recalculating the optimized contact point displacement sequences and local wear distribution data, and obtaining the contact point distribution optimization result.

[0014] As a preferred technical scheme of the application, step S1 comprises:

[0015] Obtaining tooth profile geometric parameters from gear design drawings, wherein the tooth profile geometric parameters include tooth shape angle, modulus and tooth width, obtaining tooth surface fatigue characteristics from material parameters, wherein the tooth surface fatigue characteristics include fatigue limit and material hardness, calculating contact point displacement sequences and contact point pressure distribution in the meshing process through finite element analysis, determining the spatial expression of the meshing trajectory curve in the tooth surface coordinate system, and the meshing trajectory curve represents the motion path of the contact point on the tooth surface.

[0016] As a preferred technical scheme of the application, in step S2, the trajectory node distribution is extracted from the contact point displacement sequences and the curvature distribution is calculated, comprising:

[0017] The trajectory node distribution is extracted from the contact point displacement sequences by using a sliding window algorithm, the trajectory curvature distribution at each node is calculated, the spatial position of the node in the tooth surface coordinate system is determined, the trajectory curvature distribution represents the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node.

[0018] As a preferred technical solution of the present application, in step S2, the contact point migration rate and the velocity gradient distribution are determined, comprising:

[0019] According to the trajectory node distribution, the contact point migration rate is calculated, the contact point migration rate characterizing the moving speed of the contact point on the tooth surface, the velocity gradient distribution is calculated, the velocity vector and the direction angle data at each node are obtained, the velocity vector representing the direction and size of the contact point motion, and the direction angle data characterizing the angle change of the velocity vector.

[0020] As a preferred technical solution of the present application, in step S3, the direction angle change rate in the velocity gradient distribution is judged, and the coordinates of the velocity mutation point are determined, comprising:

[0021] According to the velocity gradient distribution, the direction angle change rate is calculated, it is judged whether the direction angle change rate exceeds the preset mutation point threshold, if the preset mutation point threshold is exceeded, the velocity mutation point is determined through differential analysis, the coordinates and the time stamp of the mutation point in the tooth surface coordinate system are obtained, and the time stamp characterizes the time of the mutation point.

[0022] As a preferred technical solution of the present application, in step S3, the contact point pressure distribution at the mutation point is calculated by the Hertz contact theory, comprising:

[0023] From the mutation point coordinates and the tooth profile geometric parameters, the contact point pressure distribution at the mutation point is calculated by the Hertz contact theory, the spatial position of the stress concentration point on the tooth surface is determined, the contact point pressure distribution characterizes the stress distribution characteristics at the mutation point, and the stress concentration point characterizes the local high stress area of the tooth surface.

[0024] As a preferred technical solution of the present application, in step S4, the local wear rate is calculated by the wear rate calculation formula, comprising:

[0025] For the stress concentration point, the local wear rate is calculated by the wear rate calculation formula W=k×P×v according to the tooth surface fatigue characteristics and the contact point migration rate, W represents the wear rate, k represents the material wear coefficient, P represents the contact point pressure distribution, and v represents the contact point migration rate, the local wear distribution data of the tooth surface is obtained, and the local wear distribution data characterizes the spatial distribution of the tooth surface wear.

[0026] As a preferred technical solution of the present application, in step S5, the stress concentration point distribution of the high wear area is analyzed by dynamic finite element simulation, comprising:

[0027] According to the local wear distribution data and the contact point pressure distribution, the spatial distribution law of the tooth surface wear is analyzed by using dynamic finite element simulation, the stress concentration point distribution of the high wear area is determined, the high wear area represents the area where the tooth surface wear is serious, the curvature radius is adjusted to generate improved tooth profile geometric parameters, and the improved tooth profile geometric parameters are used for optimizing the meshing performance.

[0028] In a second aspect, the present application also provides a wear prediction system of a crane transmission system, which is used to implement the above method, and the system comprises:

[0029] A first acquisition unit is configured to acquire tooth profile geometric parameters and material fatigue characteristics from gear design parameters, determine a meshing trajectory curve and a contact point pressure distribution by finite element analysis, and acquire a contact point displacement sequence.

[0030] A determination unit is configured to extract a trajectory node distribution and calculate a curvature distribution according to the contact point displacement sequence, determine a contact point migration rate and a velocity gradient distribution based on the curvature distribution.

[0031] A calculation unit is configured to judge a directional angle change rate in the velocity gradient distribution, determine a velocity mutation point coordinate, and calculate a contact point pressure distribution at the mutation point by Hertz contact theory.

[0032] A second acquisition unit is configured to determine a stress concentration point position according to the contact point pressure distribution at the mutation point, calculate a local wear rate by a wear rate calculation formula, and acquire tooth surface local wear distribution data.

[0033] An optimization unit is configured to acquire a high wear area according to the wear distribution data, analyze the stress concentration point distribution of the high wear area by dynamic finite element simulation, adjust the curvature radius to generate improved tooth profile geometric parameters, recalculate the contact point displacement sequence and the local wear distribution data after optimization, and obtain a contact point distribution optimization result.

[0034] In a third aspect, the present application also provides a computer readable storage medium, which stores instructions, and the instructions are executed by a processor to implement the above method.

[0035] The technical scheme provided by the embodiments of the present application can have the following beneficial effects:

[0036] The application provides a wear prediction method for a crane transmission system by combining gear design, material properties and dynamic finite element simulation analysis. First, the tooth profile geometric parameters and material fatigue properties are obtained from the gear design parameters, and the meshing trajectory curve and contact point pressure distribution are determined through finite element analysis. Then, the contact point displacement sequence is extracted through the sliding window algorithm, the curvature distribution of the trajectory nodes is calculated, and the migration rate and velocity gradient distribution of the contact point are determined, which can determine the motion direction and change of the contact point, especially at the speed mutation point. The contact point pressure distribution is calculated through the Hertz contact theory, and the possible stress concentration point position is identified. The application also uses dynamic finite element simulation to analyze the high wear area in depth, predicts the wear area and the corresponding stress distribution, and optimizes the tooth profile geometric parameters by adjusting the curvature radius, thereby improving the meshing performance of the gear. The above process includes the calculation of the local wear rate, the identification of the stress concentration point and the generation of the local wear distribution data. Finally, the contact point distribution is optimized through the optimized tooth profile geometric parameters. Through the mutual cooperation between the above technical solutions, not only the wear resistance of the gear transmission system can be improved, but also a scientific basis for design optimization can be provided, the failure risk caused by wear can be reduced, the service life of the equipment can be prolonged, and the working efficiency and economy of the crane can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 A flow chart of a wear prediction method for a crane transmission system in an embodiment of the application;

[0038] Figure 2 A schematic view of a contact area of two adjacent gears in a crane transmission system in an embodiment of the application;

[0039] Figure 3 A structure diagram of a wear prediction system for a crane transmission system in an embodiment of the application. DETAILED DESCRIPTION

[0040] For a further understanding of the present application, reference will be made to the following description taken in conjunction with the accompanying drawings. The present application will be further described with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related application, and not to limit the application. In addition, it should be noted that only the parts related to the application are shown in the drawings for ease of description.

[0041] As Figure 1 , the wear prediction method for a crane transmission system in the embodiment includes:

[0042] Step S1: obtaining tooth profile geometric parameters and material fatigue properties from gear design parameters, determining meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtaining contact point displacement sequence;

[0043] Specifically, the tooth profile geometry parameters are obtained from the gear design drawings, including the tooth form angle, modulus and tooth width, the tooth surface fatigue characteristics are obtained from the material parameters, including the fatigue limit and material hardness, the contact point displacement sequence and contact point pressure distribution in the meshing process are calculated by finite element analysis, and the spatial expression of the meshing trajectory curve in the tooth surface coordinate system is determined, which represents the movement path of the contact point on the tooth surface.

[0044] Specifically, since the gear is the core component of the transmission system of the crane, the wear degree of the gear determines the wear degree of the entire transmission system, therefore, by obtaining the tooth profile geometry parameters such as the tooth form angle, modulus and tooth width from the gear design drawings, the above-mentioned geometry parameters provide preliminary geometric characteristics for calculating the contact point displacement and pressure distribution, the tooth form angle and modulus determine the meshing mode and contact characteristics of the gear, and the tooth width affects the load-carrying capacity and the distribution of the working area; the tooth surface fatigue characteristics are obtained from the material parameters, including the fatigue limit and material hardness, the fatigue limit reflects the durability of the material under long-term load, and the material hardness affects the ability of the tooth surface to resist wear and plastic deformation; by the finite element analysis method (FEA), a three-dimensional geometric model of the gear pair is established, the gear tooth profile curve is discretized into a finite number of node elements, each element contains position coordinates, material properties and boundary condition information; by using this method, the relative motion of the driving gear and the driven gear in the meshing process can be simulated, the driving gear rotates at a constant angular velocity, the driven gear rotates according to the transmission ratio, and the displacement sequence of the contact point on the tooth surface, i.e. the contact point displacement sequence, is obtained by solving the displacement vector in a unit time step; the above-mentioned unit time can be 2s, and the displacement sequence of the contact point includes radial, tangential and axial displacements, which completely describes the movement trajectory of the contact point in the meshing process.

[0045] The stress tensor of the contact area is measured by a sensor, and the pressure distribution of the contact point is further obtained, in the finite element model, the Hertz contact theory is used to calculate the contact point pressure distribution, which is usually in the form of an elliptical distribution, the maximum pressure of the contact area is located at the center of the contact area, and gradually decreases outward, the calculation of the contact pressure needs to consider the influence of parameters such as the tooth surface curvature radius, the material elastic modulus and the Poisson's ratio.

[0046] The spatial expression of the meshing trajectory curve is to establish a cylindrical coordinate system in the tooth surface coordinate system, the tooth surface coordinate system takes the gear shaft center as the origin, the radial direction as the x-axis, the tangential direction as the y-axis, and the axial direction as the z-axis, the radial coordinate of the node reflects its distance from the gear center, the tangential coordinate represents its angular position in the circumferential direction, and the axial coordinate describes its position in the tooth width direction, the meshing trajectory can fully reflect the specific position change of the contact point in the working process.

[0047] The above technical scheme, by combining the geometric design of the gear with the material properties, and using the finite element analysis method to accurately calculate the displacement and pressure of the contact point, can realize the wear analysis and optimization of the gear under high load and high frequency use conditions, further improve the service life of the gear and the reliability of the transmission system.

[0048] Step S2: extracting a trajectory node distribution and calculating a curvature distribution according to the contact point displacement sequence, determining a contact point migration rate and a velocity gradient distribution based on the curvature distribution;

[0049] In step S2, the trajectory node distribution is extracted from the contact point displacement sequence by a sliding window algorithm, the trajectory curvature distribution at each node is calculated, and the spatial position of the node in the tooth surface coordinate system is determined, the trajectory curvature distribution represents the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node.

[0050] Specifically, in order to obtain the trajectory change and curvature distribution in the meshing process of the gear, the trajectory node distribution is first extracted from the contact point displacement sequence by a sliding window algorithm, the length of the window is set according to the meshing period and the sampling frequency of the gear, and the window length can be one tenth of the meshing period, i.e. the time of one revolution of the gear, a plurality of displacement data are contained in each window, the displacement data are linearly fitted to calculate the slope and intercept parameters of the fitted straight line; when the slope of adjacent windows changes by more than a predetermined threshold, the position is marked as a trajectory node; the displacement data in the window are preprocessed to remove high-frequency noise and ensure the smoothness of the data, and the preprocessed displacement data are normalized to map the coordinates of the displacement data to a standard numerical interval; then, the discrete displacement points are continuously processed using a cubic spline interpolation method to generate smooth trajectory curve segments, and the first and second derivatives of these curve segments provide the tangent direction and curvature change information of the trajectory.

[0051] In calculating the curvature distribution, a local coordinate system at the node is established. A two-dimensional local coordinate system is established with the node position as the origin, the tangent direction of the trajectory as the positive direction of the x-axis, and the direction perpendicular to the tangent as the positive direction of the y-axis. Converting the coordinates of the trajectory points in the node neighborhood into the local coordinate system facilitates curvature calculation and geometric analysis. The establishment of the local coordinate system eliminates the influence of rotation and translation of the global coordinate system, improving the accuracy and stability of curvature calculation. By calculating the tangent vector angle change rate at the trajectory node, the curvature value can be obtained, and the circular arc fitting method is further used to calculate the curvature of the node. The above curvature value describes the geometric change of the meshing trajectory curve and represents the local change of the tooth surface during meshing. The curvature distribution is also smoothed to analyze the law of curvature change during meshing, which helps to identify the areas with concentrated curvature and sharp curvature change, which are the most likely to be worn. Finally, the local coordinates of the node are converted into three-dimensional coordinates in the tooth surface coordinate system through a coordinate transformation matrix. The coordinate transformation considers the geometric parameters of the gear, including the modulus, pressure angle, helix angle, and number of teeth. The three-dimensional coordinates of the node include radial coordinates, tangential coordinates, and axial coordinates, which completely describe the spatial position of the node on the tooth surface. The above technical scheme accurately describes the trajectory change and curvature distribution during gear meshing, providing reliable data support for gear wear prediction in the transmission system of the crane.

[0052] Further, in step S2, the contact point migration rate and the velocity gradient distribution are determined, including:

[0053] According to the trajectory node distribution, the contact point migration rate is calculated, which represents the moving speed of the contact point on the tooth surface, and the velocity gradient distribution is calculated, obtaining the velocity vector and direction angle data at each node. The velocity vector represents the direction and size of the contact point motion, and the direction angle data represents the angle change of the velocity vector.

[0054] Specifically, according to the trajectory node distribution, the contact point migration rate is calculated, which is used to represent the moving speed of the contact point on the tooth surface, specifically including:

[0055] According to the spatial coordinate difference of adjacent nodes in the trajectory node distribution, the displacement vector between the nodes is calculated. By extracting the three-dimensional coordinate data of each trajectory node from the tooth surface coordinate system, the displacement components between adjacent nodes are determined using vector operations. The displacement vector contains components in the radial, tangential, and axial directions. The three-dimensional coordinate data of each trajectory node is extracted through vector operations to ensure the accuracy of the position calculation and reflect the actual movement path of the contact point on the tooth surface;

[0056] The time interval data during the meshing process is combined to calculate the instantaneous migration rate at each node by the ratio of displacement vector to time interval. The time interval data is derived from the discretization of the gear meshing period, which divides the continuous meshing process into several time steps. The instantaneous migration rate reflects the speed of the contact point at a specific time, providing data support for subsequent stress analysis and wear prediction.

[0057] The instantaneous migration rate of adjacent nodes is smoothed by using the weighted average method to eliminate the sudden noise in numerical calculation. The weighting coefficient is determined according to the distance between nodes and the contact pressure distribution. Nodes with closer distance and similar pressure have higher weight. The smoothed migration rate data has better continuity.

[0058] Based on the calculated migration rate, the velocity gradient distribution of the contact point is further calculated, including obtaining the velocity vector and direction angle data at each node. The specific process is as follows:

[0059] Based on the migration rate data at each node, the spatial distribution of velocity gradient is calculated using the finite difference method. The finite difference method calculates the rate of change of velocity in space in each direction through the difference operation of velocity values between adjacent nodes. The velocity gradient includes radial gradient, tangential gradient, and normal gradient, which are the three components of the velocity gradient, representing the change characteristics of velocity in different directions of the tooth surface. The radial gradient reflects the change of velocity along the direction from the dedendum to the addendum. The tangential gradient reflects the change of velocity along the direction of the tooth profile curve. The normal gradient reflects the change of velocity perpendicular to the tooth surface.

[0060] According to the size and direction information of the migration rate, the velocity vector at each node is constructed. The modulus of the velocity vector is equal to the value of the migration rate, and the vector direction is determined by the moving direction of the contact point. The velocity vector is expressed as a component form in the tooth surface coordinate system through vector decomposition, which facilitates subsequent numerical calculation and analysis.

[0061] The angle between the velocity vector and the reference direction of the tooth surface coordinate system is calculated to obtain the direction angle data at each node. The reference direction is usually selected as the tangent direction or radial direction of the tooth profile as a reference. The direction angle data is expressed in radians, with a value range of 0 to 2π. The spatial distribution of the direction angle can identify the change rule and abnormal area of the motion direction of the contact point.

[0062] The spatial differential operation of the direction angle data is performed by the gradient operator to calculate the rate of change of the direction angle. The gradient operator includes partial differential operation, which calculates the rate of change of the direction angle in each direction of the tooth surface coordinate system. The rate of change of the direction angle reflects the stability of the motion direction of the contact point. The area with a larger rate of change indicates that the motion direction of the contact point changes sharply, which may have the risk of stress concentration or wear intensification.

[0063] The above-mentioned technical solution can accurately calculate the migration rate and velocity gradient distribution of gear contact points, providing important basic data for predicting gear wear in crane transmission systems. This method can effectively identify abrupt changes in the motion of contact points, help predict areas of concentrated wear, and thus provide a scientific basis for optimizing gear design, thereby extending the service life of gears and improving the reliability and stability of crane transmission systems.

[0064] Step S3: Determine the rate of change of the direction angle in the velocity gradient distribution, determine the coordinates of the velocity abrupt change point, and use Hertz contact theory to calculate the pressure distribution at the contact point at the abrupt change point;

[0065] In step S3, determining the rate of change of the direction angle in the velocity gradient distribution and determining the coordinates of the velocity abrupt change point includes:

[0066] Based on the velocity gradient distribution, the rate of change of the direction angle is calculated, and it is determined whether the rate of change of the direction angle exceeds a preset threshold for abrupt change. If it exceeds the preset threshold for abrupt change, the velocity abrupt change point is determined through differential analysis, and the coordinates and timestamp of the abrupt change point in the tooth surface coordinate system are obtained. The timestamp represents the time when the abrupt change point occurs.

[0067] Specifically, based on the velocity gradient distribution, the rate of change of the direction angle at each trajectory node is first calculated. Based on the migration rate and velocity gradient distribution at the contact point, the velocity vector direction angle data at each node is extracted, and the direction angle difference between adjacent nodes is calculated. The rate of change of the direction angle is then solved using the finite difference method, with the specific formula as follows:

[0068]

[0069] in, Indicates the first The orientation angle of each node For the corresponding time parameters, in actual implementation, if the distribution density of trajectory nodes is high, a three-point difference format is used to improve the calculation accuracy. For boundary nodes, the rate of change of their orientation angle can be processed by weighted average.

[0070] The calculated rate of change of the orientation angle at each node is compared with a preset threshold for abrupt change. The preset threshold for abrupt change is set based on the gear meshing characteristics and tooth surface fatigue characteristics, for example, the set range is 0.5 rad / ms to 2.0 rad / ms. In this embodiment, for gears with different gear modules and pressure angles, the threshold for abrupt change is set in segments, for example, the threshold for small module gears is 0.8 rad / ms, and the threshold for large module gears is 1.2 rad / ms. When the absolute value of the rate of change of the orientation angle at a certain node exceeds the preset threshold, the node is marked as a potential abrupt change.

[0071] For the potential mutation point of the label, second-order difference analysis is performed to determine the precise position of the mutation point. The rate of change of the rate of change of the direction angle is calculated by the central difference format, and the formula is as follows:

[0072]

[0073] When the second derivative value changes in sign and the amplitude exceeds the preset second-order threshold, it is confirmed that the point is a real speed mutation point, and the second-order threshold is usually set to 5.0 radians per millisecond squared to ensure accurate identification of the speed jump phenomenon in the meshing process.

[0074] The precise coordinates of the mutation point in the tooth surface coordinate system are calculated by an interpolation method, and a cubic spline interpolation algorithm is used to calculate the x, y, z coordinate values of the mutation point based on the coordinate data of the two nodes before and after the mutation point. In an embodiment, when the mutation point is located between two trajectory nodes, a Lagrange interpolation polynomial can be used for accurate calculation.

[0075] The tooth surface coordinate system is established with the gear shaft center as the origin, the radial direction as the x-axis, the tangential direction as the y-axis, and the axial direction as the z-axis to ensure accurate expression of the mutation point coordinates.

[0076] The timestamp represents the time when the mutation point occurs, and the precise time of the mutation point in the meshing period is calculated by a linear interpolation method, and the specific formula is as follows:

[0077]

[0078] where λ is an interpolation ratio determined by the relative position of the mutation point coordinates between the two nodes, and are the time parameters of the two nodes before and after the mutation point, respectively. Preferably, the accuracy of the timestamp can be set to 0.01 milliseconds to meet the time resolution requirements of gear dynamic meshing analysis. In a preferred embodiment, for the meshing process of a helical gear, since the contact line moves gradually along the tooth width direction, the identification of the speed mutation point needs to consider the influence of the helix angle, and a helix angle correction coefficient is introduced when calculating the rate of change of the direction angle. The correction coefficient is cos(β), where β is the helix angle. For example, for a helical gear with a helix angle of 30 degrees, the correction coefficient is 0.866, and the mutation point threshold is adjusted to 1.15 times the original value to ensure the accuracy of the mutation point identification.

[0079] The above technical solution can accurately identify the speed mutation point of the contact point in the gear meshing process, providing key data for wear prediction in the crane transmission system, and can also effectively identify the change in the motion direction of the contact point and provide accurate position and time information of the mutation point, thereby providing a scientific basis for gear design optimization, wear analysis and life prediction, and improving the reliability and durability of the crane transmission system.

[0080] Further, in step S3, the contact point pressure distribution at the mutation point is calculated by Hertz contact theory, including:

[0081] According to the mutation point coordinates and the tooth profile geometric parameters, the contact point pressure distribution at the mutation point is calculated by Hertz contact theory to determine the spatial position of the stress concentration point on the tooth surface, and the stress concentration point represents a local high stress area on the tooth surface.

[0082] Specifically, according to the coordinate data of the mutation point and the tooth profile geometric parameters, a contact geometry model is established. By extracting the spatial position of the mutation point in the tooth surface coordinate system and combining the tooth surface curvature radius, contact angle and normal vector data in the tooth profile geometric parameters, a local contact geometry model at the mutation point is constructed, which includes:

[0083] The principal curvature radii R1 and R2 are the principal curvature radii of the driving gear and the driven gear at the mutation point, i.e. the local curvature radii of the tooth surfaces of the driving gear and the driven gear.

[0084] The relative curvature radius which is calculated by the formula:

[0085]

[0086] It is also necessary to determine the long axis direction and the short axis direction of the contact ellipse at the contact point, and these geometric parameters will provide basic data for Hertz contact pressure calculation.

[0087] Based on the Hertz contact theory, as shown in Figure 2 , it is assumed that the contact area is elliptical and the contact pressure is distributed in an ellipsoidal shape within the elliptical area. According to the relative curvature radius and the material elastic modulus in the contact geometry model, the semi-major axis a and the semi-minor axis b of the contact ellipse are calculated, and their geometric dimensions are calculated by the elliptic integral function, and the specific formula is as follows:

[0088]

[0089] where F is the contact load, E is the equivalent elastic modulus, v is the Poisson's ratio, m and n are preset parameters of the ellipse, and the pressure distribution function of any point in the contact area is:

[0090]

[0091] where p0 is the maximum contact pressure, and the above-mentioned center of the contact area ellipse is taken as the origin, and the straight lines where the major axis and the minor axis lie are taken as the coordinate axes, where x and y are the coordinates within the contact ellipse. m reflects the elastic properties of the contact ellipse in the major axis direction, and n reflects the elastic properties of the contact ellipse in the minor axis direction, and m and n are related to the elastic modulus of the contact surface.

[0092] According to the Hertz contact theory, the maximum contact pressure p0 is located at the center of the contact ellipse, and its value is:

[0093]

[0094] The maximum contact pressure p0 represents the contact strength at the mutation point, and the pressure gradient distribution is calculated by the spatial partial derivative of the pressure distribution function, and the specific calculation formula is:

[0095]

[0096] The modulus of the pressure gradient is:

[0097]

[0098] Where, the area with larger pressure gradient corresponds to the position where the stress concentration phenomenon is more significant.

[0099] The stress concentration point is the area in the contact pressure distribution where the modulus of the pressure gradient exceeds the preset stress concentration threshold By traversing all the grid points in the contact ellipse, the modulus of the pressure gradient of each point is calculated. When the modulus of the pressure gradient of a point is greater than the set threshold, the point is marked as a stress concentration candidate point. After clustering analysis of all candidate points, points with a spatial distance less than the clustering radius are classified into the same stress concentration area, and the geometric center of each area is taken as the stress concentration point of the area.

[0100] The above technical solution realizes accurate calculation of the contact point pressure distribution at the mutation point during gear meshing, and identifies the position of the stress concentration point through pressure gradient analysis. This method not only accurately evaluates the contact pressure and stress distribution during gear meshing, but also provides a scientific basis for further crane transmission system wear prediction, tooth profile optimization, and gear design.

[0101] Step S4: Determine the position of the stress concentration point, calculate the local wear rate by the wear rate calculation formula, and obtain the local wear distribution data of the tooth surface;

[0102] In step S4, the local wear rate is calculated by the wear rate calculation formula, including:

[0103] Based on the stress concentration point, the local wear rate is calculated by the wear rate calculation formula W=k×P×v, combining the fatigue characteristics of the tooth surface and the migration rate of the contact point, where W represents the wear rate, k represents the material wear coefficient, P represents the contact point pressure distribution, and v represents the migration rate of the contact point. Obtain the local wear distribution data of the tooth surface, which represents the spatial distribution of the tooth surface wear.

[0104] Specifically, based on the stress concentration point coordinates and the tooth surface geometric parameters, the precise position of the stress concentration point on the tooth surface is determined. Specifically, the spatial position of the stress concentration point is converted from the coordinates of the contact area corresponding to the elliptical coordinate system to the coordinates in the tooth surface coordinate system, ensuring accurate positioning of the stress concentration point in the tooth surface coordinate system. Based on the above stress concentration point, by extracting the basic mechanical performance parameters of the gear material, including the elastic modulus, Poisson's ratio, yield strength, and fatigue limit, and combining the S-N curve fitting of the material fatigue test data, the horizontal axis and the vertical axis represent the stress size applied to the material and the fatigue life, i.e., the number of cycles that the material can withstand under the corresponding stress size. The above S-N curve, i.e., the stress-life curve, can determine the fatigue life characteristics of the material under different stress levels. A fatigue damage accumulation function is established to describe the fatigue damage evolution law of the tooth surface material under cyclic loading. In addition, the fatigue characteristic parameters are combined with the tooth surface hardness distribution, surface roughness, and residual stress distribution to construct a spatial distribution function of the tooth surface fatigue characteristics.

[0105] Based on the meshing trajectory curve and the trajectory node distribution, the instantaneous velocity vector at each trajectory node is calculated by numerical differentiation method. The velocity vector is decomposed into tangential component and normal component, where the tangential component represents the sliding rate of the contact point along the tooth surface, and the normal component represents the approaching and separating rate of the contact point. Combined with the gear speed and transmission ratio parameters, the time variation law of the contact point migration rate in the meshing period is calculated. The discrete rate data is expanded to the entire tooth surface area by interpolation algorithm, forming a continuous distribution field of the contact point migration rate.

[0106] The time and space distribution characteristics of the contact point migration rate are calculated. Based on the meshing trajectory curve and the trajectory node distribution, the instantaneous velocity vector at each trajectory node is calculated by numerical differentiation method. The velocity vector is decomposed into tangential component and normal component, where the tangential component represents the sliding rate of the contact point along the tooth surface, and the normal component represents the approaching and separating rate of the contact point. Combined with the gear speed and transmission ratio parameters, the time variation law of the contact point migration rate in the meshing period is calculated. The discrete rate data is expanded to the entire tooth surface area by interpolation algorithm, forming a continuous distribution field of the contact point migration rate.

[0107] The wear rate calculation formula is applied to calculate the local wear rate. The material wear coefficient k, the contact point pressure distribution P, and the contact point migration rate v are substituted into the wear rate calculation formula W=k×P×v. The local wear rate values at each position on the tooth surface are obtained by point-by-point calculation.

[0108] A tooth surface local wear distribution data structure is constructed. The calculated local wear rate values are arranged according to the tooth surface coordinate positions to form a wear rate distribution matrix. The row index of the matrix corresponds to the position in the tooth width direction, the column index corresponds to the position in the tooth height direction, and the matrix element value is the wear rate value at the corresponding position. The wear rate distribution matrix is visualized by the contour drawing method to identify the spatial distribution characteristics of the high wear area and the low wear area. Statistical characteristic parameters of the wear distribution data are established, including the average wear rate, the wear rate standard deviation and the wear concentration index, which are used to quantify the spatial distribution law of the tooth surface wear.

[0109] For example, in an embodiment, for the wear rate calculation of a straight tooth cylindrical gear, the stress concentration points are mainly distributed in the tooth root transition fillet area and the tooth surface area near the pitch line. The tooth root transition fillet area has a high stress concentration coefficient due to the sharp change in the geometric shape, and the contact pressure in this area can reach 2.3 times the average contact pressure. The area near the pitch line has a relatively low contact point migration rate, and the sliding friction effect is significant, resulting in an increase in the contribution of the velocity term in the wear rate calculation. Through comparative analysis, it is found that the wear in the tooth root area is mainly dominated by high contact pressure, while the wear in the pitch line area is determined by the coupling effect of the contact point migration rate and the pressure.

[0110] In another possible implementation, the wear distribution of the helical gear presents a spiral characteristic, which is closely related to the tooth surface spiral angle and the inclination distribution of the contact line. For a helical gear with a spiral angle of 30 degrees, the contact point migration rate has a clear gradient distribution in the tooth width direction, and the migration rate at both ends of the tooth width is about 15% higher than that in the middle. The non-uniformity of this rate distribution causes the tooth surface wear to present an increasing trend from the middle to both ends of the tooth width. Combined with the spatial variation of the tooth surface fatigue characteristics, the local wear distribution data of the helical gear shows a complex three-dimensional spatial distribution pattern, which requires the use of a three-dimensional interpolation algorithm for data processing and analysis.

[0111] In the wear rate calculation, the tooth surface fatigue characteristics and the dynamic influence of the wear coefficient are combined. When the tooth surface material undergoes a certain number of cyclic loads, the surface microstructure changes, causing the material wear coefficient to exhibit time-varying characteristics. When the fatigue damage accumulates to a certain extent, the wear coefficient can increase to 1.8 times the initial value, thereby affecting the calculation results of the local wear rate.

[0112] The spatial distribution characteristics of the local wear distribution data reflect the spatial pattern of energy dissipation during the gear meshing process. High wear areas correspond to locations with high energy dissipation density, and these areas are usually the starting point of gear failure. By analyzing the spatial gradient and concentration characteristics of the wear distribution, the weak links in the gear design can be identified, providing quantitative basis for tooth profile modification and material optimization. The wear distribution data can also be correlated with the gear vibration characteristics and noise level to achieve the coordinated optimization of the overall performance of the gear.

[0113] Step S5: analyze the stress concentration point distribution of the high wear area by dynamic finite element simulation, adjust the curvature radius to generate improved tooth profile geometric parameters, recalculate the optimized contact point displacement sequence and local wear distribution data, and obtain the contact point distribution optimization result.

[0114] In step S5, the stress concentration point distribution of the high wear area is analyzed by dynamic finite element simulation, including:

[0115] According to the local wear distribution data and the contact point pressure distribution, a dynamic simulation model is created, and based on the dynamic simulation model, the spatial distribution law of tooth surface wear is analyzed by dynamic finite element simulation to determine the high wear area and the corresponding stress concentration point distribution. The high wear area represents the area where the tooth surface wears severely, and the curvature radius is adjusted to generate improved tooth profile geometric parameters for optimizing the meshing performance.

[0116] Specifically, the implementation of the above technical solution includes the following steps:

[0117] (1) Establish a dynamic simulation model of tooth surface wear, input the local wear distribution data as boundary conditions to the finite element grid nodes, and map the contact point pressure distribution to the corresponding tooth surface grid elements; the dynamic finite element simulation model uses Lagrange description method to establish the tooth surface geometric model, and the grid density is locally encrypted in the expected high wear area to improve the calculation accuracy of this area. The simulation model considers the elastic-plastic deformation characteristics of the material, and uses a bilinear kinematic hardening model to describe the stress-strain relationship of the material under cyclic loading.

[0118] (2) Set the dynamic load boundary conditions. According to the time-varying characteristics of the gear meshing process, the contact point pressure distribution is time-discretized according to the meshing period. The load size and direction in each time step are determined according to the contact point pressure distribution and the meshing position. The load is applied in the form of node force, and the tooth root constraint condition is set to limit the radial and tangential displacement degrees of freedom of the tooth root nodes, and the overall stiffness characteristics of the gear are maintained.

[0119] (3) Perform dynamic finite element solution calculation, and use Newmark time integration method to solve the dynamic response of the tooth surface under cyclic loading. During the solution process, the stress state of each grid node is monitored, and the distribution of principal stress, shear stress and equivalent stress is particularly concerned. The stress tensor of each point on the tooth surface at different times is calculated to form the time and space distribution data of the tooth surface stress field.

[0120] (4) Based on the stress field distribution data and the local wear distribution data, the spatial distribution law of tooth surface wear is identified. Through comparative analysis, it is found that the severe wear area usually corresponds to the position with higher stress concentration coefficient, and the stress gradient change in these areas is more violent. The spatial distribution law of wear presents non-uniform distribution characteristics along the tooth height direction, especially in the pitch circle and the transition area of tooth top and tooth root, the wear degree is relatively high.

[0121] (5) Determine the determination criteria of high wear area, define the area with local wear rate exceeding 1.5 times of the average wear rate as high wear area, i.e. predicted wear data, high wear area is usually distributed near the peak point of tooth surface contact stress and the position with large change of contact trajectory curvature. The characteristics of these areas are obvious stress concentration phenomenon, fast material fatigue damage accumulation speed and severe wear.

[0122] (6) Identify the stress concentration point distribution in the high wear area. The spatial coordinates of local stress peak point are determined by using stress gradient analysis method. The identification of stress concentration point is based on equivalent stress distribution, and the nodes with equivalent stress value exceeding 0.8 times of material yield strength are selected as potential stress concentration points. By calculating the stress concentration coefficient of each node, the nodes with stress concentration coefficient greater than 2.0 are determined as key stress concentration points, and their position information in the tooth surface coordinate system is recorded.

[0123] Further, from the stress concentration point distribution of high wear area, combined with the velocity gradient distribution, the curvature radius is adjusted and corrected to generate improved tooth profile geometric parameters, which are used to optimize the meshing performance. Specifically, it includes:

[0124] (1) Analyze the correlation between stress concentration points and tooth profile curvature radius. Through geometric analysis, it is found that stress concentration points usually appear in positions with small tooth profile curvature radius. The size of curvature radius directly affects the distribution of contact stress, the smaller the curvature radius, the greater the contact stress, and the more likely to form stress concentration phenomenon.

[0125] (2) According to the velocity gradient distribution, determine the adjustment strategy of curvature radius. In the area with violent change of velocity gradient, the curvature radius is appropriately increased to reduce the peak value of contact stress. The calculation of curvature radius adjustment amount is based on Hertz contact theory, and the reasonable curvature radius value is determined by controlling the maximum contact stress not to exceed the material allowable stress.

[0126] (3) Generate improved tooth profile geometric parameters. Including the corrected tooth profile curve equation, tooth top circle radius, tooth root circle radius and transition arc radius and other key geometric dimensions. The improved tooth profile geometric parameters optimize the contact stress distribution and reduce the occurrence of stress concentration phenomenon while keeping the gear transmission ratio unchanged.

[0127] The technical scheme has the advantages that the high-wear area and wear prediction data and corresponding stress concentration point distribution are obtained and analyzed through the dynamic simulation model and the dynamic finite element algorithm simulation, and the tooth profile curvature radius is adjusted based on the stress concentration point and the velocity gradient distribution to generate improved tooth profile geometric parameters, so that the meshing performance of the gear is effectively optimized, the wear resistance of the gear is improved, and the service life of the gear is prolonged, and meanwhile, the wear distribution can be accurately predicted based on the identification of the high-wear area, thereby providing a basis for gear design and material optimization.

[0128] The application further provides a wear prediction system of a crane transmission system for implementing the above method. Figure 3 As shown in the figure, the system comprises:

[0129] A first acquisition unit is configured to acquire tooth profile geometric parameters and material fatigue characteristics from gear design parameters, determine meshing trajectory curves and contact point pressure distribution through finite element analysis, and acquire contact point displacement sequences.

[0130] A determination unit is configured to extract trajectory node distribution and calculate curvature distribution according to the contact point displacement sequences, determine contact point migration rate and velocity gradient distribution based on the curvature distribution.

[0131] A calculation unit is configured to judge the direction angle change rate in the velocity gradient distribution, determine the coordinates of the velocity mutation point, and calculate the contact point pressure distribution at the mutation point through the Hertz contact theory.

[0132] A second acquisition unit is configured to determine the stress concentration point position according to the contact point pressure distribution at the mutation point, calculate the local wear rate through a wear rate calculation formula, and acquire tooth surface local wear distribution data.

[0133] An optimization unit is configured to acquire a high-wear area according to the wear distribution data, analyze the stress concentration point distribution of the high-wear area through dynamic finite element simulation, adjust the curvature radius to generate improved tooth profile geometric parameters, recalculate the contact point displacement sequences and the local wear distribution data after optimization, and obtain a contact point distribution optimization result.

[0134] The application further provides a computer readable storage medium, wherein the computer readable storage medium stores instructions, and the instructions are executed by a processor to implement the above method.

[0135] In summary, the application provides a wear prediction method for the crane transmission system by combining gear design, material properties and dynamic finite element simulation analysis. Firstly, the tooth profile geometric parameters and material fatigue characteristics are obtained from the gear design parameters, and the meshing trajectory curve and contact point pressure distribution are determined through finite element analysis. Then, the contact point displacement sequence is extracted through the sliding window algorithm, the curvature distribution of the trajectory node is calculated, and the migration rate and velocity gradient distribution of the contact point are determined, which can determine the motion direction and change of the contact point, especially at the speed mutation point. The contact point pressure distribution is calculated through the Hertz contact theory, and the possible stress concentration point position is identified. The application also uses dynamic finite element simulation to analyze the high wear area in depth, predicts the wear area and the corresponding stress distribution, and optimizes the tooth profile geometric parameters by adjusting the curvature radius, thereby improving the meshing performance of the gear. The above process includes the calculation of the local wear rate, the identification of the stress concentration point and the generation of the local wear distribution data. Finally, the contact point distribution is optimized through the optimized tooth profile geometric parameters. Through the mutual cooperation between the above technical solutions, not only the wear resistance of the gear transmission system can be improved, but also a scientific basis for design optimization can be provided, the risk of failure caused by wear can be reduced, the service life of the equipment can be prolonged, and the working efficiency and economy of the crane can be improved.

[0136] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present application without departing from the spirit and scope of the embodiments of the present application. Thus, if these modifications and variations of the embodiments of the present application belong to the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. A method for wear prediction of a hoist drive system, characterized by, The method comprises the following steps: Step S1: obtaining tooth profile geometry parameters and material fatigue characteristics from gear design parameters, determining meshing trajectory curve and contact point pressure distribution through finite element analysis, and obtaining contact point displacement sequence; Step S2: extracting trajectory node distribution and calculating curvature distribution according to the contact point displacement sequence, and determining contact point migration rate and velocity gradient distribution based on the curvature distribution; wherein the trajectory node distribution is extracted from the contact point displacement sequence by using a sliding window algorithm, the trajectory curvature distribution at each node is calculated, the spatial position of the node in the tooth surface coordinate system is determined, the trajectory curvature distribution represents the geometric change of the meshing trajectory curve, and the spatial position includes the three-dimensional coordinates of the node; The determination of the contact point migration rate and the velocity gradient distribution comprises: calculating the contact point migration rate according to the trajectory node distribution, the contact point migration rate representing the moving speed of the contact point on the tooth surface, calculating the velocity gradient distribution, obtaining the velocity vector and the direction angle data at each node, the velocity vector representing the direction and size of the motion of the contact point, and the direction angle data representing the angle change of the velocity vector; Step S3: judging the direction angle change rate in the velocity gradient distribution, determining the coordinates of the velocity mutation point, and calculating the contact point pressure distribution at the mutation point through the Hertz contact theory; wherein the determination of the direction angle change rate in the velocity gradient distribution and the coordinates of the velocity mutation point comprises: calculating the direction angle change rate according to the velocity gradient distribution, judging whether the direction angle change rate exceeds a preset mutation point threshold, if the direction angle change rate exceeds the preset mutation point threshold, determining the velocity mutation point through difference analysis, obtaining the coordinates and time stamp of the mutation point in the tooth surface coordinate system, and the time stamp representing the time when the mutation point occurs; The calculation of the contact point pressure distribution at the mutation point through the Hertz contact theory comprises: calculating the contact point pressure distribution at the mutation point through the Hertz contact theory from the mutation point coordinates and the tooth profile geometry parameters, determining the spatial position of the stress concentration point on the tooth surface, the contact point pressure distribution representing the stress distribution characteristics at the mutation point, and the stress concentration point representing the local high stress area of the tooth surface; Step S4: determining the stress concentration point position according to the contact point pressure distribution at the mutation point, calculating the local wear rate through the wear rate calculation formula, and obtaining the local wear distribution data of the tooth surface; Step S5: obtaining the high wear area according to the local wear distribution data, the contact point pressure distribution and the dynamic simulation model, taking the high wear area as the wear prediction data, analyzing the stress concentration point distribution of the high wear area through dynamic finite element simulation, adjusting the curvature radius to generate improved tooth profile geometry parameters, recalculating the optimized contact point displacement sequence and local wear distribution data, and obtaining the contact point distribution optimization result.

2. The method of claim 1, wherein, Step S1 comprises: Obtaining tooth profile geometry parameters from gear design drawings, the tooth profile geometry parameters including a tooth form angle, a module and a tooth width, obtaining tooth surface fatigue characteristics from material parameters, the tooth surface fatigue characteristics including a fatigue limit and a material hardness, calculating a contact point displacement sequence and a contact point pressure distribution in a meshing process by a finite element analysis method, and determining a spatial expression of an engagement locus curve in a tooth surface coordinate system, the engagement locus curve representing a movement path of the contact point on the tooth surface.

3. The method of claim 1, wherein, In step S4, a local wear rate is calculated by a wear rate calculation formula, including: For a stress concentration point, a local wear rate is calculated by a wear rate calculation formula W=k×P×v in combination with tooth surface fatigue characteristics and a contact point migration rate, W represents a wear rate, k represents a material wear coefficient, P represents a contact point pressure distribution, and v represents a contact point migration rate, and tooth surface local wear distribution data is obtained, the tooth surface local wear distribution data representing a spatial distribution of tooth surface wear.

4. The method of claim 1, wherein, In step S5, a stress concentration point distribution of a high wear area is analyzed by dynamic finite element simulation, including: According to the local wear distribution data and the contact point pressure distribution, a spatial distribution rule of tooth surface wear is analyzed by dynamic finite element simulation, a stress concentration point distribution of a high wear area is determined, the high wear area represents a region with severe tooth surface wear, a curvature radius is adjusted to generate improved tooth profile geometry parameters, and the improved tooth profile geometry parameters are used to optimize meshing performance.

5. A wear prediction system of a hoist drive system for implementing the method according to any one of claims 1 - 4, characterized by The system comprises: A first obtaining unit is configured to obtain tooth profile geometry parameters and material fatigue characteristics from gear design parameters, determine an engagement locus curve and a contact point pressure distribution by finite element analysis, and obtain a contact point displacement sequence; A determining unit is configured to extract a locus node distribution and calculate a curvature distribution according to the contact point displacement sequence, determine a contact point migration rate and a velocity gradient distribution based on the curvature distribution; A calculating unit is configured to determine a velocity mutation point coordinate by judging a direction angle change rate in the velocity gradient distribution, and calculate a contact point pressure distribution at the mutation point by Hertz contact theory; A second obtaining unit is configured to determine a stress concentration point position according to the contact point pressure distribution at the mutation point, calculate a local wear rate by a wear rate calculation formula, and obtain tooth surface local wear distribution data; An optimization unit is configured to obtain a high wear area according to the wear distribution data, analyze a stress concentration point distribution of the high wear area by dynamic finite element simulation, adjust a curvature radius to generate improved tooth profile geometry parameters, recalculate a contact point displacement sequence and local wear distribution data after optimization, and obtain a contact point distribution optimization result.

6. A computer-readable storage medium having stored thereon instructions, the computer-readable storage medium comprising: The instructions are executed by the processor to implement the method of any one of claims 1-4. The instructions are executed by the processor to implement the method of any one of claims 1-4.

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