A strong honing process tooth surface appearance positive prediction method
By replicating the surface morphology of the honing wheel and processing the data, combined with Boolean operations and a prediction model, the problem of low prediction accuracy in high-strength honing was solved, and high-precision prediction of the gear tooth surface of the workpiece was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUNAN UNIV
- Filing Date
- 2024-03-21
- Publication Date
- 2026-06-19
Smart Images
Figure CN118123136B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of mechanical processing and manufacturing technology, specifically relating to a positive prediction method for tooth surface morphology in a high-strength honing process. Background Technology
[0002] The performance of gear products directly depends on the quality of the surface layer after machining. High-intensity honing is typically the final process in the gear manufacturing chain, aiming to eliminate tooth profile deformation and achieve the required geometric accuracy and surface quality. High-intensity honing surface quality forward prediction technology is of great significance in improving processing efficiency, optimizing product performance, saving resources and costs, and guiding industrial applications.
[0003] Due to differences in workpiece geometry and machining principles, the prediction model for surface quality in high-power honing differs fundamentally from that in surface grinding. In related technologies, high-power honing surface quality prediction techniques, to simplify calculations, assume complex random abrasive grains to be ideal spheres. While this prediction establishes a mapping relationship between tooth surface morphology and gear tooth profile, the assumptions and simplifications in this prediction cause a certain discrepancy between the simulation results and the actual machined surface morphology, resulting in low prediction accuracy.
[0004] Therefore, it is necessary to provide a positive prediction method for the tooth surface morphology of high-strength honing processes to solve the problems mentioned in the background art. Summary of the Invention
[0005] This application provides a positive prediction method for the tooth surface morphology of a high-strength honing process, which can accurately reflect the surface morphology of the honing wheel and achieve accurate prediction of the tooth surface morphology of the workpiece gear.
[0006] To solve the above-mentioned technical problems, the technical solution of this application is as follows:
[0007] A method for positively predicting the tooth surface morphology in a high-strength honing process includes the following steps:
[0008] Step S1: Obtain the surface morphology data of the honing wheel based on the surface replication method;
[0009] Step S2: In the spatial coordinate system of the high-power honing machine tool, based on the coordinate position relationship between the honing wheel and the workpiece gear during the high-power honing process, the surface morphology data of the honing wheel is mapped to the coordinate system of the workpiece gear.
[0010] Step S3: Generate the theoretical smooth tooth surface of the workpiece gear and divide it into a mesh. Treat the interaction between the honing wheel and the workpiece gear as a Boolean operation of subtracting the spatial trajectory of the abrasive grains on the honing wheel from that of the workpiece gear. Calculate the grinding amount UCT of the abrasive grains on the workpiece gear at any time. If UCT is greater than 0, replace the coordinates of the mesh points with the coordinates of the abrasive grains at that time; otherwise, keep the coordinates of the mesh points unchanged. Update the mesh in real time to obtain the surface morphology data of the workpiece gear after strong honing.
[0011] Step S4: Construct a prediction model by inputting the tooth profile parameters of the workpiece gear, the machining parameters in the high-power honing process, the surface morphology data of the honing wheel, and the surface morphology data of the workpiece gear after high-power honing into the prediction model for training until the model converges.
[0012] Step S5: For any one strong honing process, the tooth profile parameters of the workpiece gear, the machining parameters in the strong honing process, and the surface morphology data of the honing wheel are input into the prediction model for prediction, and the predicted value of the surface morphology data of the workpiece gear after strong honing is output.
[0013] Preferably, step S1 specifically includes the following steps:
[0014] Step S11: A replica is formed by completely replicating any single tooth of the honing wheel using vinyl polysiloxane material. The local surface of the replica is scanned using a white light interferometer to obtain the local surface morphology data of the replica.
[0015] Step S12: Evaluate whether the local surface morphology data of the replica conforms to a normal distribution. If so, interpolate based on the local surface morphology data of the replica to obtain the complete surface morphology data of the replica. If not, use Johnson transform to convert the local surface morphology data of the replica into standard normally distributed data, then interpolate based on the transformed data, and finally use inverse Johnson transform to obtain the complete surface morphology data of the replica.
[0016] Step S13: The complete surface morphology data of the replica is equivalently extended to all teeth of the honing wheel to obtain the surface morphology data of the honing wheel.
[0017] Preferably, the Johnson transform process is represented as follows:
[0018]
[0019] In the formula, z represents the transformed standard normal distribution data; x represents the measurement data; sinh -1(·) represents the inverse hyperbolic sine function; γ and η represent the transformation coefficients, which determine the shape of the distribution; ε represents the center offset; and α represents the scaling factor.
[0020] The process of the inverse Johnson transform is represented as follows:
[0021]
[0022] Preferably, the mapping relationship between the surface topography data of the honing wheel and the workpiece gear coordinate system is expressed as follows:
[0023] r2(λ,θ;t)=M 21 (t)r1(λ,θ);
[0024] In the formula, r2(λ,θ;t) represents the coordinates of the honing wheel in the workpiece gear coordinate system at time t; M 21 (t) represents the transformation relationship from the honing wheel coordinate system to the workpiece gear coordinate system at time t; r1(λ,θ) represents the coordinates of the workpiece gear in the workpiece gear coordinate system; θ represents the helical surface heave angle; λ represents the unfolding angle;
[0025]
[0026] In the formula, and ∑ represents the rotation angle of the workpiece gear and the honing wheel, respectively; ∑ represents the axial angle between the axis of the workpiece gear and the axis of the honing wheel.
[0027] Preferably, the tooth profile parameters of the workpiece gear include module, number of teeth, pressure angle, and helix angle; the machining parameters in the high-strength honing process include honing wheel speed, honing wheel feed speed, and honing depth. The beneficial effects of this application are:
[0028] (1) By using vinyl polysiloxane to replicate the surface morphology of the honing wheel, the true morphology of the honing wheel can be obtained, which effectively solves the problem of low prediction accuracy caused by assuming complex random abrasive particles as ideal spheres in the prior art.
[0029] (2) By using Boolean operations to calculate the surface morphology of the honing wheel, a large amount of data can be generated for subsequent prediction training, thereby further improving the accuracy of prediction. Attached Figure Description
[0030] Figure 1 This document presents a flowchart illustrating the honing wheel tooth surface modeling method based on the surface replication method provided in this application.
[0031] Figure 2 This application shows a rubbing of the surface morphology of the honing wheel provided in this application;
[0032] Figure 3A flowchart illustrating the forward prediction method for tooth surface morphology in the high-strength honing process provided in this application;
[0033] Figure 4 This indicates the deviation between the predicted values provided in this application and the experimental values. Detailed Implementation
[0034] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0035] Please refer to the following: Figures 1-4 This application provides a method for positive prediction of tooth surface morphology in a high-strength honing process, comprising the following steps:
[0036] Step S1: Obtain the surface morphology data of the honing wheel based on the surface replication method.
[0037] Specifically, the steps include the following:
[0038] Step S11: A replica is formed by completely replicating any single tooth of the honing wheel using vinyl polysiloxane material. The local surface of the replica is scanned using a white light interferometer to obtain the local surface morphology data of the replica.
[0039] Step S12: Evaluate whether the local surface morphology data of the replica conforms to a normal distribution. If so, interpolate based on the local surface morphology data of the replica to obtain the complete surface morphology data of the replica. If not, use Johnson transform to convert the local surface morphology data of the replica into standard normally distributed data, then interpolate based on the transformed data, and finally use inverse Johnson transform to obtain the complete surface morphology data of the replica.
[0040] Step S13: The complete surface morphology data of the replica is equivalently extended to all teeth of the honing wheel to obtain the surface morphology data of the honing wheel.
[0041] A single tooth of a honing wheel is replicated using vinyl polysiloxane material. The grains on the replica are used to replace the abrasive grains on the honing wheel. The surface morphology of the honing wheel replica is obtained by measuring the grain height on the replica, and this is used to characterize the surface morphology of the honing wheel.
[0042] Because the scanning microscope of a white light interferometer has a small measurement range, measuring the entire surface morphology of a honing wheel replica would be extremely time-consuming. Furthermore, the manufacturing process of the honing wheel results in a random process where the distribution and shape of abrasive grains on its surface follow certain statistical laws. Therefore, this application chooses to reconstruct the local measurement data of the honing wheel replica using a Johnson model based on local measurements to shorten the measurement time. Due to lens limitations, the scanning microscope of the white light interferometer can only measure a small area at a time. Therefore, a stitching method is needed to stitch together multiple scanning areas to obtain sufficient original morphology data.
[0043] The Johnson transform process can be represented as follows:
[0044]
[0045] In the formula, z represents the transformed standard normal distribution data; x represents the measurement data; sinh -1 (·) represents the inverse hyperbolic sine function, γ and η represent the transformation coefficients that determine the shape of the distribution; ε represents the center offset; and α represents the scaling factor.
[0046] After substituting the values, we get:
[0047]
[0048] The process of the inverse Johnson transform is represented as follows:
[0049]
[0050] After substituting the values, we get:
[0051]
[0052] The complete surface morphology data H of the replica can be represented by a 50×1047 matrix:
[0053]
[0054] In the formula, h eg,(i,j) This represents the grain height at coordinate (i,j).
[0055] In a honing wheel, the surface morphology of each tooth is kept consistent. Therefore, the obtained surface morphology data of a single tooth can be equivalently extended to all teeth to obtain the surface morphology data of the honing wheel.
[0056] Step S2: In the spatial coordinate system of the high-power honing machine tool, based on the coordinate position relationship between the honing wheel and the workpiece gear during the high-power honing process, the surface morphology data of the honing wheel is mapped to the coordinate system of the workpiece gear.
[0057] In the spatial coordinate system of a high-power gear honing machine, the transformation relationship M from the honing wheel coordinate system to the workpiece gear coordinate system. 21 Represented as:
[0058]
[0059] In the formula, and ∑ represents the rotation angle of the workpiece gear and the honing wheel, respectively; ∑ represents the axial angle between the axis of the workpiece gear and the axis of the honing wheel;
[0060] The standard equation for the helical involute tooth surface of a workpiece gear is expressed as:
[0061]
[0062] In the formula, θ represents the helical involute angle; p represents the lead of the helical involute; and b1 represents the width of the workpiece gear. Indicates the root circle radius of the gear in the workpiece; Indicates the radius of the addendum circle of the gear in the workpiece; λ represents the base circle radius of the workpiece gear; λ represents the development angle.
[0063] The equation for maintaining conjugate meshing between the honing wheel and the workpiece gear is:
[0064]
[0065] The above expression simplifies to:
[0066]
[0067] The equation for the tooth surface of the honing wheel is then expressed as:
[0068]
[0069]
[0070] In the formula, r2(λ,θ;t) represents the coordinates of the honing wheel in the workpiece gear coordinate system at time t; M 21 (t) represents the transformation relationship from the honing wheel coordinate system to the workpiece gear coordinate system at time t; r1 represents the coordinates of the workpiece gear in the workpiece gear coordinate system, and r2 represents the coordinates of the honing wheel in the workpiece gear coordinate system.
[0071] The ideal involute tooth surface of a workpiece gear can be enveloped in space by the developing motion of an ideal honing wheel surface. However, the actual tooth surface morphology of a honed workpiece gear is formed by the grinding and removal action of numerous abrasive grains on the honing wheel. Therefore, it is necessary to construct a computational model to map the morphology of the honing wheel onto the microscopic morphology of the tooth surface.
[0072] The high-intensity honing process can be simulated by time discretization to analyze the interaction between the honing wheel and the gear workpiece at different times.
[0073] At time t, the position of any cutting edge point on the honing wheel in the gear workpiece coordinate system can be expressed as:
[0074] r2(λ,θ;t)=M 21 (t)r1(λ,θ).
[0075] Step S3: Generate the theoretical smooth tooth surface of the workpiece gear and divide it into a mesh. Treat the interaction between the honing wheel and the workpiece gear as a Boolean operation of subtracting the spatial trajectory of the abrasive grains on the honing wheel from that of the workpiece gear. Calculate the grinding amount UCT of the abrasive grains on the workpiece gear at any time. If UCT is greater than 0, replace the coordinates of the mesh points with the coordinates of the abrasive grains at that time; otherwise, keep the coordinates of the mesh points unchanged. Update the mesh in real time to obtain the surface morphology data of the workpiece gear after strong honing.
[0076] During the grinding process of the honing wheel on the workpiece gear, when the grinding amount UCT is greater than 0, it indicates that the abrasive grains and the surface of the workpiece gear have interacted. After the interaction, the coordinates of the grid points on the surface of the workpiece gear are consistent with the coordinates of the abrasive grains. Conversely, it indicates that the abrasive grains and the surface of the workpiece gear have not interacted, and the coordinates of the grid points remain at their initial values.
[0077] Step S4: Construct a prediction model by inputting the tooth profile parameters of the workpiece gear, the machining parameters in the high-power honing process, the surface morphology data of the honing wheel, and the surface morphology data of the workpiece gear after high-power honing into the prediction model for training until the model converges.
[0078] Repeating steps S1-S3 can generate a large amount of data for model training, which can improve the model's prediction accuracy.
[0079] The tooth profile parameters of the workpiece gear include module, number of teeth, pressure angle, and helix angle; the machining parameters in the high-strength honing process include honing wheel speed, honing wheel feed speed, and honing depth.
[0080] Step S5: For any one strong honing process, the tooth profile parameters of the workpiece gear, the machining parameters in the strong honing process, and the surface morphology data of the honing wheel are input into the prediction model for prediction, and the predicted value of the surface morphology data of the workpiece gear after strong honing is output.
[0081] The effectiveness of the prediction method provided in this application was verified by experiments. The measured surface morphology data of the workpiece gear was compared with the surface morphology data predicted by this application. The maximum error was found to be 10.45%, indicating that the prediction method provided in this application can effectively predict the tooth surface morphology in the high-strength honing process.
[0082] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.
Claims
1. A method for forward prediction of tooth surface topography in a power honing process, characterized in that, Includes the following steps: Step S1: Obtain the surface morphology data of the honing wheel based on the surface replication method; Step S2: In the spatial coordinate system of the high-power honing machine tool, based on the coordinate position relationship between the honing wheel and the workpiece gear during the high-power honing process, the surface morphology data of the honing wheel is mapped to the coordinate system of the workpiece gear. Step S3: Generate the theoretical smooth tooth surface of the workpiece gear and divide it into a mesh. Treat the interaction between the honing wheel and the workpiece gear as a Boolean operation of subtracting the spatial trajectory of the abrasive grains on the honing wheel from that of the workpiece gear. Calculate the grinding amount UCT of the abrasive grains on the workpiece gear at any time. If UCT is greater than 0, replace the coordinates of the mesh points with the coordinates of the abrasive grains at that time; otherwise, keep the coordinates of the mesh points unchanged. Update the mesh in real time to obtain the surface morphology data of the workpiece gear after strong honing. Step S4: Construct a prediction model by inputting the tooth profile parameters of the workpiece gear, the machining parameters in the high-power honing process, the surface morphology data of the honing wheel, and the surface morphology data of the workpiece gear after high-power honing into the prediction model for training until the model converges. Step S5: For any strong honing process, the tooth profile parameters of the workpiece gear, the processing parameters in the strong honing process, and the surface morphology data of the honing wheel are used as inputs to the prediction model for prediction, and the predicted value of the surface morphology data of the workpiece gear after strong honing is output. Step S1 specifically includes the following steps: Step S11: A replica is formed by completely replicating any single tooth of the honing wheel using vinyl polysiloxane material. The local surface of the replica is scanned using a white light interferometer to obtain the local surface morphology data of the replica. Step S12: Evaluate whether the local surface morphology data of the replica conforms to a normal distribution. If yes, interpolate based on the local surface morphology data of the replica to obtain the complete surface morphology data of the replica. If no, use Johnson transform to convert the local surface morphology data of the replica into standard normally distributed data, then interpolate based on the transformed data, and finally use inverse Johnson transform to obtain the complete surface morphology data of the replica. Step S13: The complete surface morphology data of the replica is equivalently extended to all teeth of the honing wheel to obtain the surface morphology data of the honing wheel.
2. The method of forward prediction of gear tooth surface topography for a power honing process of claim 1, wherein, The Johnson transform process can be represented as follows: ； In the formula, This represents the transformed standard normal distribution data; Represents measurement data; Represents the inverse hyperbolic sine function. , The conversion coefficient represents the distribution shape; Indicates the center offset; Indicates the scaling factor; The process of the inverse Johnson transform is represented as follows: 。 3. The method for positive prediction of tooth surface morphology in high-strength honing process according to claim 1, characterized in that, The mapping relationship between the surface topography data of the honing wheel and the workpiece gear coordinate system is expressed as follows: ； In the formula, This represents the coordinates of the honing wheel in the workpiece gear coordinate system at time t; This represents the transformation relationship from the honing wheel coordinate system to the workpiece gear coordinate system at time t; This indicates the coordinates of the workpiece gear in the workpiece gear coordinate system; Indicates the helix angle; Indicates the development angle; ； In the formula, and These represent the rotation angles of the workpiece gear and the honing wheel, respectively. This indicates the axial angle between the workpiece gear axis and the honing wheel axis.
4. The method for positive prediction of tooth surface morphology in high-strength honing process according to claim 1, characterized in that, The tooth profile parameters of the workpiece gear include module, number of teeth, pressure angle, and helix angle; the machining parameters in the high-strength honing process include honing wheel speed, honing wheel feed speed, and honing depth.