Method for characterizing wear state and predicting remaining life of honing grinding wheel for strong honing

Abstract

The invention provides a method for characterizing the wear state of a honing wheel for strong honing and predicting the remaining life. The method aligns the predicted fractal dimension with the measured tooth surface quality detection results in time, constructs a quality out-of-tolerance probability model, and directly converts the prediction of tool wear state into a measurable tooth surface quality out-of-tolerance risk quantitative index, overcoming the deficiency that the existing method is disconnected between the wheel state characterization and the product quality evaluation, and providing a clear quality constraint basis for the decision of the dressing timing. By establishing an expected comprehensive cost function including the dressing cost, downtime cost and quality loss cost, the optimal dressing timing is determined under the premise of meeting the quality out-of-tolerance probability constraint, with the goal of minimizing the unit effective processing cost, avoiding the problems of resource waste caused by premature dressing and quality loss caused by late dressing which depend on artificial experience to judge the dressing timing, and realizing the full utilization of the honing wheel life and the effective guarantee of the processing quality.

Description

Technical Field

[0001] This invention relates to the fields of precision gear machining and grinding wheel condition characterization, and particularly to a method for characterizing the wear condition and predicting the remaining life of honing grinding wheels for high-power gear honing. Background Technology

[0002] Honing is a crucial process in precision gear manufacturing, widely used in automotive transmission systems, aerospace reducers, and industrial robot joints—applications demanding high transmission precision and low noise levels. Internal meshing high-strength honing involves a honing wheel, shaped like an internal gear, forcibly meshing with an external gear workpiece. The relative slippage between the two achieves minute material removal from the tooth surface, creating a herringbone-like texture and high residual compressive stress. This significantly improves the gear's load-bearing capacity and transmission smoothness, making it an irreplaceable core process in high-speed, low-noise precision gear machining. The honing wheel, as the key functional carrier in this process, directly determines the machining efficiency and workpiece surface quality through the morphology and distribution of its abrasive grains. Therefore, the wear state of the honing wheel has a crucial impact on the stability of the entire process.

[0003] However, during long-term service, honing wheels are continuously affected by thermal coupling, causing various forms of damage to their surface abrasive grains, such as wear and dulling, breakage and shedding, and wear debris adhesion. This leads to a continuous degradation of the grinding capability of the wheel, and the surface quality of the machined workpieces deteriorates gradually with the increase of cumulative machining volume. If the wear state of the grinding wheel is not monitored in time and dressed at the appropriate time, it may result in a large number of workpieces having out-of-tolerance surface quality or even being scrapped, causing serious economic losses. Therefore, how to accurately and timely characterize the wear state of honing wheels and predict their remaining life is a key technical problem to ensure the stable operation of high-strength honing processes. In the field of grinding wheel wear condition monitoring, existing technologies can be mainly divided into two categories: online monitoring methods based on external sensors and offline characterization methods based on surface morphology description.

[0004] A. In terms of online monitoring, devices such as acoustic emission sensors, vibration acceleration sensors, and machine vision cameras have been widely used in general grinding applications such as surface grinding and cylindrical grinding. These devices can collect acoustic signals, vibration signals, or image information in real time during the machining process and combine signal processing and machine learning methods to determine the wear state of the grinding wheel. However, due to the special closed internal meshing structure of heavy-duty gear honing machines, the machining area is extremely limited, which greatly restricts the installation of the aforementioned external sensors. Existing sensor layout schemes are difficult to directly transplant and apply, severely limiting the applicability of online monitoring technology in gear honing processes.

[0005] B. In terms of offline characterization, some studies have used elastomer materials such as vinyl polysiloxane to imprint the surface of grinding wheels and combined this with precision measuring equipment such as laser profilometers to obtain the surface morphology data of the grinding wheels. Then, indicators such as fractal dimension are used to quantitatively describe the wear state, which has achieved certain application results on gear grinding tools such as worm wheels. However, existing methods still have several shortcomings in engineering applications: First, imprint measurement lacks a strict positioning and reproduction mechanism, and the morphology data collected at different measurement times are difficult to correspond to the same position on the grinding wheel, resulting in poor longitudinal comparability of state sequences; Second, existing degradation models are mostly based on curve fitting of the number of processed parts under a single process condition, failing to effectively reflect the influence of changes in process parameters such as spindle speed and feed rate on the grinding wheel degradation trajectory, and lacking cross-condition adaptability; Third, existing methods usually treat the grinding wheel state characterization and workpiece tooth surface quality evaluation independently, lacking a predictive mechanism that directly links the grinding wheel wear state with the risk of tooth surface quality deviation, making it difficult to provide effective support for quantitative decision-making on dressing timing.

[0006] Therefore, there is an urgent need to propose a more complete and practical method for characterizing the wear state and predicting the remaining life of honing wheels. Summary of the Invention

[0007] The purpose of this invention is to provide a method for characterizing the wear state and predicting the remaining life of honing grinding wheels for high-power honing, so as to solve the problems existing in the prior art.

[0008] The technical solution adopted to achieve the purpose of this invention is as follows: a method for characterizing the wear state and predicting the remaining life of a honing wheel for high-power honing, comprising the following steps:

[0009] S1) Honing wheel positioning, imprinting, and contour data acquisition. Tooth markings are established on the honing wheel, and the effective contact area is defined as the repeatable measurement area using tooth and axial positioning references. Before processing and after processing a preset number of workpieces, the machine is stopped, and vinyl polysiloxane material is used to imprint the repeatable measurement area. After the imprint samples are cured, a laser profilometer is used to acquire multiple two-dimensional contour curves, and the number of processed parts and measurement conditions are recorded.

[0010] S2) Contour Fractal Dimension Calculation and Degradation Trend Modeling. The collected contour curves are sequentially processed by detrending, filtering, and effective region truncation. The power spectral density method is used to calculate the fractal dimension of each contour. Statistically representative values ​​of the fractal dimensions of multiple contours at the same measurement moment are taken as the fractal wear state at that moment, thus obtaining the historical state sequence of the honing wheel. Based on the historical state sequences under multiple process conditions, a degradation trend model of the fractal dimension changing with the cumulative number of processed parts is established.

[0011] S3) Construct a fractal dimension time-series prediction model. Using the historical fractal dimension sequence, the cumulative number of processed parts sequence, and process parameters as inputs, and the degradation trend model established in step S2) as a constraint term added to the loss function, train the time-series prediction model to predict the fractal dimension changes and the probability of tooth surface quality deviations in future processing stages.

[0012] S4) Calculation of Remaining Life and Determination of Dressing Timing. The fractal dimension of different processing stages is time-aligned with the corresponding workpiece tooth surface quality inspection results to establish a mapping relationship between fractal wear state and tooth surface quality deviation probability. Based on the future fractal dimension sequence predicted in step S3), the tooth surface quality deviation probability for each future processing stage is calculated. When the deviation probability first reaches a preset threshold, the honing wheel life warning point is determined and the remaining number of workpieces is calculated. Combining dressing costs, downtime costs, and quality loss costs, the dressing timing with the lowest overall cost is determined.

[0013] Furthermore, step S1) specifically includes the following sub-steps:

[0014] S1.1) A central composite design is used to construct an experimental matrix, covering the range of commonly used process parameters in actual production. These process parameters include spindle speed, axial feed rate, radial feed rate, and the number of sparkless honing passes. Each process combination completes a full dressing cycle for a preset number of gears.

[0015] S1.2) After processing a preset number of workpieces, stop the machine and use vinyl polysiloxane material for rubbing under the same positioning conditions, and record the material type, curing time, ambient temperature, contact pressure and repeatability error. Use a laser profilometer to scan the rubbing sample and extract no less than 5 parallel contour curves in each positioning area.

[0016] S1.3) Redundant data in non-contact areas are removed, median filtering is used to remove scanning noise, and the installation tilt error is eliminated by fitting the baseline using the least squares method to obtain standardized contour height data.

[0017] Furthermore, step S2) specifically includes the following sub-steps:

[0018] S2.1) The fractal dimension D is calculated using the power spectral density method. The standardized contour height data is detrended to eliminate the influence of macroscopic shape on the spectral analysis. A discrete Fourier transform is performed on the detrended data to calculate the power spectral density. The frequency index is converted to spatial frequency and angular wavenumber. Within a scale range excluding the lowest frequency macroscopic shape and noise close to the Nyquist frequency, the relationship between the power spectral density and wavenumber is fitted by linear regression in a double logarithmic coordinate system to obtain the power spectral density exponent β. The contour is used only when the goodness of fit R² meets the preset requirements, and the fractal dimension D is calculated using the following formula: .

[0019] S2.2) Calculate the fractal dimension for multiple profiles at the same measurement time, and use the mean, median, or truncated mean as the statistical representative value, and record the standard deviation, thereby constructing the historical state sequence of the honing wheel. .

[0020] S2.3) Based on data from multiple independent life cycles, a degradation trend model of the fractal dimension as a function of the cumulative number of processed parts is established. For working conditions with an initial increase and a later decrease, the following double power law form is adopted:

[0021]

[0022] In the formula, u=[n,f z ,f x Let [,d] be the process parameter vector, D0 be the initial fractal dimension, c1(u) and c2(u) be coefficients related to the process parameters, and α1 and α2 be power-law exponents, with constraints c1(u)>0, c2(u)>0, and α2>α1>0. c1(u) and c2(u) are represented by low-order response surfaces containing main effects and necessary interaction terms. When the experimental data do not support the double power-law form, piecewise monotonic splines or generalized additive models with inflection points are used instead.

[0023] Furthermore, step S3) specifically includes the following sub-steps:

[0024] S3.1) Define the model input and output. The model input includes the historical fractal state sequence up to the current moment. Corresponding cumulative processing volume Process parameters The model output includes batch parameters such as the abrasive grain size of the honing wheel and the type of bonding agent. It also includes the fractal dimension sequence for future machining stages and tooth surface quality indicators or the probability of quality deviations.

[0025] S3.2) Model Structure Design. The temporal prediction model adopts a Transformer encoder architecture. The historical fractal dimension, cumulative number of processed parts, and process parameters are mapped into multi-dimensional feature vectors through the input embedding layer, which are then fused with the positional encoding of the number of processed parts to form temporal input features. A multi-layer, multi-head self-attention mechanism is employed to capture the long-range dependencies between different wear stages. An adaptive weight module for life stages is set up, dividing the honing wheel life into three stages: initial, middle, and late. During training, later samples are assigned higher dynamic weights. A multi-task output layer is set up, with the main branch outputting the predicted fractal dimension value for the future processing stage, and the auxiliary branch outputting tooth surface quality indicators or the probability of quality deviation.

[0026] S3.3) Design the joint loss function. The joint loss function of the time series prediction model is:

[0027]

[0028] in, The mean square error of the fractal dimension prediction. To account for the consistency error between the predicted trajectory and the statistical degradation model, This is the prediction error for tooth surface quality. , This is the balance coefficient. The dataset is grouped according to a complete honing wheel or a complete dressing cycle. The test set must not contain adjacent test points of the same honing wheel from the training set.

[0029] S3.4) Training and updating of time series prediction models.

[0030] Furthermore, the training and updating method of the time series prediction model is as follows: Time series cross-validation is used to divide the model into training, validation, and test sets to avoid leakage of time series information. The AdamW optimizer is used for training, and an early stopping strategy is implemented. After accumulating a preset batch of new experimental data, only the model's attention weights and output layer parameters are updated to achieve incremental training and adapt to process adjustment requirements.

[0031] Furthermore, step S4) specifically includes the following sub-steps:

[0032] S4.1) Construct the out-of-range probability input feature vector ,in The fractal dimension of the current processing stage. This represents the change in fractal dimension between adjacent sampling stages. The rate of fractal dimension degradation. This represents the number of parts already processed. This includes batch-level parameters such as honing wheel material, abrasive grain size, binder type, and workpiece material. A logistic regression model is used to establish the probability of quality deviation.

[0033]

[0034] The model parameters are obtained through training using the cross-entropy loss function.

[0035] S4.2) In the current processing stage The time series prediction model established in step S3) is used to predict the future fractal dimension sequence. By combining the quality deviation probability model established with the corresponding process parameters input in S4.1, the quality deviation probability sequence for each future processing stage is obtained. Determine the lifespan warning point.

[0036] S4.3) Establish the expected comprehensive cost function that includes repair costs, downtime costs, and quality loss costs. Assume processing continues from the current stage. After finishing, the unit effective processing cost is:

[0037]

[0038] in, To fix repair costs, Cost per unit downtime This refers to the downtime for a single maintenance operation. Cost per unit of quality loss To prevent extremely small positive numbers with a denominator of zero. While satisfying... ( Under the constraints of ), take smallest Therefore, the recommended number of parts to be processed at the appropriate repair time is: .

[0039] Furthermore, the number of remaining processed parts is calculated using the following formula:

[0040]

[0041] in, This represents the current number of pieces processed. For the first time in the predicted quality out-of-range probability sequence to satisfy The corresponding number of processed parts at that time This is the preset threshold for the probability of quality deviation.

[0042] The technical effects of this invention are beyond doubt:

[0043] A. Repeatable positioning measurement of the surface morphology of honing wheels was achieved. By establishing tooth markings on the honing wheel and defining the effective contact area using tooth direction and axial positioning references, and using vinyl polysiloxane material for imprinting, it is ensured that each measurement targets the same location area on the grinding wheel surface. This overcomes the shortcomings of existing offline characterization methods, such as poor spatial correspondence and insufficient longitudinal comparability of morphology data at different measurement times, and significantly improves the temporal consistency and reliability of wear state sequences.

[0044] B. Improved robustness of fractal wear indices to the randomness of single contours. By extracting multiple parallel contour curves within the same location area and using statistically representative values ​​to characterize the current wear state, the random errors introduced by local defects or measurement noise in a single contour are effectively reduced. This makes the fractal dimension more stable and reliable as a wear health indicator, providing a high-quality data foundation for subsequent degradation trend modeling.

[0045] C. Degradation trajectory correction under cross-working conditions was achieved. By incorporating process parameter vectors into the degradation trend model, a statistical degradation model was established in which the fractal dimension changes jointly with the cumulative number of processed parts and process parameters. This overcomes the limitations of existing methods that can only fit degradation curves under a single process condition and have insufficient adaptability across working conditions, enabling degradation trend prediction to cover scenarios where process parameters such as spindle speed and feed rate change in actual production.

[0046] D. Effectively integrate statistical degradation prior knowledge into time series prediction models. By introducing the degradation trend model as a regularization constraint into the joint loss function of the time series Transformer model, the data-driven prediction results maintain physical consistency with the known wear trend, avoiding the prediction divergence problem that easily occurs in pure data-driven models when training data is limited, and improving the prediction accuracy and generalization ability of the model in the later stages of life. Attached Figure Description

[0047] Figure 1 The overall flowchart of the honing wheel life prediction method;

[0048] Figure 2 A schematic diagram of the imprinting method for vinyl polysiloxane materials and laser profilometry scanning. Figure 2 a is a schematic diagram of the vinyl polysiloxane material imprinting method; Figure 2 b is a schematic diagram of obtaining two-dimensional contour curve data by scanning the imprint sample using a laser profilometer;

[0049] Figure 3 is a flowchart of the structure of the temporal Transformer model;

[0050] Figure 4 is a scatter plot comparing the predicted and actual values;

[0051] Figure 5 shows a comparison between the predicted fractal dimension curve and the actual measured value;

[0052] Figure 6 shows the probability of quality deviation and the timing of repair. Detailed Implementation

[0053] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0054] Example 1:

[0055] See Figure 1 This embodiment provides a method for characterizing the wear state and predicting the remaining life of a honing wheel for high-power honing, including the following steps:

[0056] S1) Honing wheel positioning, imprinting, and contour data acquisition. Tooth markings are established on the honing wheel, and the effective contact area is defined as the repeatable measurement area using tooth and axial positioning references. Before processing and after processing a preset number of workpieces, the machine is stopped, and vinyl polysiloxane material is used to imprint the repeatable measurement area. After the imprint samples are cured, a laser profilometer is used to acquire multiple two-dimensional contour curves, and the number of processed parts and measurement conditions are recorded.

[0057] S2) Contour Fractal Dimension Calculation and Degradation Trend Modeling. The collected contour curves are sequentially processed by detrending, filtering, and effective region truncation. The power spectral density method is used to calculate the fractal dimension of each contour. Statistically representative values ​​of the fractal dimensions of multiple contours at the same measurement moment are taken as the fractal wear state at that moment, thus obtaining the historical state sequence of the honing wheel. Based on the historical state sequences under multiple process conditions, a degradation trend model of the fractal dimension changing with the cumulative number of processed parts is established.

[0058] S3) Construct a fractal dimension time-series prediction model. Using the historical fractal dimension sequence, the cumulative number of processed parts sequence, and process parameters as inputs, and the degradation trend model established in step S2) as a constraint term added to the loss function, train the time-series prediction model to predict the fractal dimension changes and the probability of tooth surface quality deviations in future processing stages.

[0059] S4) Calculation of Remaining Life and Determination of Dressing Timing. The fractal dimension of different processing stages is time-aligned with the corresponding workpiece tooth surface quality inspection results to establish a mapping relationship between fractal wear state and tooth surface quality deviation probability. Based on the future fractal dimension sequence predicted in step S3), the tooth surface quality deviation probability for each future processing stage is calculated. When the deviation probability first reaches a preset threshold, the honing wheel life warning point is determined and the remaining number of workpieces is calculated. Combining dressing costs, downtime costs, and quality loss costs, the dressing timing with the lowest overall cost is determined.

[0060] Example 2:

[0061] The main content of this embodiment is the same as that of Embodiment 1, wherein step S1) specifically includes the following sub-steps:

[0062] S1.1) A central composite design is used to construct an experimental matrix, covering the range of commonly used process parameters in actual production. These process parameters include spindle speed, axial feed rate, radial feed rate, and the number of sparkless honing passes. Each process combination completes a full dressing cycle for a preset number of gears.

[0063] S1.2) After processing a preset number of workpieces, stop the machine and use vinyl polysiloxane material for rubbing under the same positioning conditions, and record the material type, curing time, ambient temperature, contact pressure and repeatability error. Use a laser profilometer to scan the rubbing sample and extract no less than 5 parallel contour curves in each positioning area.

[0064] S1.3) Redundant data in non-contact areas are removed, median filtering is used to remove scanning noise, and the installation tilt error is eliminated by fitting the baseline using the least squares method to obtain standardized contour height data.

[0065] Example 3:

[0066] The main content of this embodiment is the same as that of embodiment 1 or 2, wherein step S2) specifically includes the following sub-steps:

[0067] S2.1) The fractal dimension D is calculated using the power spectral density method. The standardized contour height data is detrended to eliminate the influence of macroscopic shape on the spectral analysis. A discrete Fourier transform is performed on the detrended data to calculate the power spectral density. The frequency index is converted to spatial frequency and angular wavenumber. Within a scale range excluding the lowest frequency macroscopic shape and noise close to the Nyquist frequency, the relationship between the power spectral density and wavenumber is fitted by linear regression in a double logarithmic coordinate system to obtain the power spectral density exponent β. The contour is used only when the goodness of fit R² meets the preset requirements, and the fractal dimension D is calculated using the following formula: .

[0068] S2.2) Calculate the fractal dimension for multiple profiles at the same measurement time, and use the mean, median, or truncated mean as the statistical representative value, and record the standard deviation, thereby constructing the historical state sequence of the honing wheel. .

[0069] S2.3) Based on data from multiple independent life cycles, a degradation trend model of the fractal dimension as a function of the cumulative number of processed parts is established. For working conditions with an initial increase and a later decrease, the following double power law form is adopted:

[0070]

[0071] In the formula, u=[n,f z ,f x Let [,d] be the process parameter vector, D0 be the initial fractal dimension, c1(u) and c2(u) be coefficients related to the process parameters, and α1 and α2 be power-law exponents, with constraints c1(u)>0, c2(u)>0, and α2>α1>0. c1(u) and c2(u) are represented by low-order response surfaces containing main effects and necessary interaction terms. When the experimental data do not support the double power-law form, piecewise monotonic splines or generalized additive models with inflection points are used instead.

[0072] Example 4:

[0073] The main content of this embodiment is the same as any one of embodiments 1 to 3, wherein step S3) specifically includes the following sub-steps:

[0074] S3.1) Define the model input and output. The model input includes the historical fractal state sequence up to the current moment. Corresponding cumulative processing volume Process parameters The model output includes batch parameters such as the abrasive grain size of the honing wheel and the type of bonding agent. It also includes the fractal dimension sequence for future machining stages and tooth surface quality indicators or the probability of quality deviations.

[0075] S3.2) Model Structure Design. The temporal prediction model adopts a Transformer encoder architecture. The historical fractal dimension, cumulative number of processed parts, and process parameters are mapped into multi-dimensional feature vectors through the input embedding layer, which are then fused with the positional encoding of the number of processed parts to form temporal input features. A multi-layer, multi-head self-attention mechanism is employed to capture the long-range dependencies between different wear stages. An adaptive weight module for life stages is set up, dividing the honing wheel life into three stages: initial, middle, and late. During training, later samples are assigned higher dynamic weights. A multi-task output layer is set up, with the main branch outputting the predicted fractal dimension value for the future processing stage, and the auxiliary branch outputting tooth surface quality indicators or the probability of quality deviation.

[0076] S3.3) Design the joint loss function. The joint loss function of the time series prediction model is:

[0077]

[0078] in, The mean square error of the fractal dimension prediction. To account for the consistency error between the predicted trajectory and the statistical degradation model, This is the prediction error for tooth surface quality. , This is the balance coefficient. The dataset is grouped according to a complete honing wheel or a complete dressing cycle. The test set must not contain adjacent test points of the same honing wheel from the training set.

[0079] S3.4) Training and updating of time series prediction models.

[0080] Example 5:

[0081] The main content of this embodiment is the same as any one of embodiments 1 to 4. The training and updating method of the time series prediction model is as follows: Time series cross-validation is used to divide the training set, validation set, and test set to avoid leakage of time series information. The AdamW optimizer is used for training, and an early stopping strategy is implemented. After each preset batch of new experimental data is accumulated, only the attention weights and output layer parameters of the model are updated to achieve incremental training and adapt to the needs of process adjustment.

[0082] Example 6:

[0083] The main content of this embodiment is the same as any one of embodiments 1 to 5. Step S4) specifically includes the following sub-steps:

[0084] S4.1) Construct the out-of-range probability input feature vector ,in The fractal dimension of the current processing stage. This represents the change in fractal dimension between adjacent sampling stages. The rate of fractal dimension degradation. This represents the number of parts already processed. This includes batch-level parameters such as honing wheel material, abrasive grain size, binder type, and workpiece material. A logistic regression model is used to establish the probability of quality deviation.

[0085]

[0086] The model parameters are obtained through training using the cross-entropy loss function.

[0087] S4.2) In the current processing stage The time series prediction model established in step S3) is used to predict the future fractal dimension sequence. By combining the quality deviation probability model established with the corresponding process parameters input in S4.1, the quality deviation probability sequence for each future processing stage is obtained. Determine the lifespan warning point. The remaining number of processed parts is calculated using the following formula:

[0088]

[0089] in, This represents the current number of pieces processed. For the first time in the predicted quality out-of-range probability sequence to satisfy The corresponding number of processed parts at that time This is the preset threshold for the probability of quality deviation.

[0090] S4.3) Establish the expected comprehensive cost function that includes repair costs, downtime costs, and quality loss costs. Assume processing continues from the current stage. After finishing, the unit effective processing cost is:

[0091]

[0092] in, To fix repair costs, Cost per unit downtime This refers to the downtime for a single maintenance operation. Cost per unit of quality loss To prevent extremely small positive numbers with a denominator of zero. While satisfying... ( Under the constraints of ), take smallest Therefore, the recommended number of parts to be processed at the appropriate repair time is: .

[0093] Example 7:

[0094] This embodiment uses an input shaft gear and its matching honing wheel for a certain type of new energy vehicle transmission as the implementation object. Its normal module is 1.4 mm, the tooth pressure angle is 20°, the number of teeth is 51, and the material is 20CrMnTi. The honing wheel parameters are: abrasive grain size 120#, number of teeth 113. (The rest of the text appears to be unrelated and possibly machine-generated.) Figure 1 As shown, this embodiment provides a method for characterizing the wear state and predicting the remaining life of a grinding wheel used for high-power honing, including the following steps:

[0095] Step 1: Honing wheel positioning, rubbing, and contour data acquisition. Step 1, specifically, involves:

[0096] The experimental scheme was constructed using a central composite design, and the process parameter ranges are shown in the table below.

[0097]

[0098] An experimental matrix was constructed using a central composite design (CCD) to cover the range of commonly used process parameters in actual production. Each process combination completed the full dressing cycle of gear A.

[0099] Step 102: Mark the tooth number on the honing wheel and define the effective contact area using tooth direction and axial positioning references. Stop the machine after processing every 10 gears and use vinyl polysiloxane material to make a rubbing under the same positioning conditions. Record the curing time as 5 minutes and the ambient temperature as 20°C. Record the honing wheel tooth number, axial positioning position, tooth direction positioning position, and number of processed parts for each rubbing.

[0100] A laser profilometer is used to scan the imprint sample and obtain two-dimensional contour curve data, specifically as follows: Figure 2As shown. Five parallel contours are extracted in each positioning area; if necessary, contours perpendicular to the tooth direction are added to evaluate directionality. Redundant data in non-contact areas are removed, median filtering is used to remove scanning noise, and the installation tilt error is eliminated by fitting the baseline using the least squares method to obtain standardized contour height data z(x).

[0101] Step 2: Contour fractal dimension calculation and degradation trend modeling. Step 2, specifically the contour fractal dimension calculation and degradation trend modeling, involves:

[0102] Step 201: Fractal dimension is a quantitative indicator describing the complexity and space-filling degree of fractal structures. It measures the irregularity and complexity of the contour curve and is used to evaluate the contour morphology. The fractal dimension D of the standardized contour data is calculated using the power spectral density method, and the specific steps are as follows.

[0103] (1) First, the data is detrended to eliminate the influence of sample tilt or macroscopic shape on the spectral analysis. The original contour height data is z(x), where x is the position coordinate. The detrended contour data is calculated using the following formula:

[0104]

[0105] In the formula, a and b are linear regression coefficients, and z1(x) is the detrended profile data.

[0106] (2) Perform a discrete Fourier transform: Perform a Fourier transform on z1(x) to obtain the spectral coefficients F(x) as follows:

[0107]

[0108] In the formula, N is the total number of data points.

[0109] (3) The power spectral density is calculated by the square of the modulus of the Fourier coefficients, as shown in the following formula:

[0110]

[0111] In the formula, △x is the sampling interval.

[0112] (4) Convert the frequency index to the spatial frequency:

[0113]

[0114] In the formula, f is the spatial frequency and kwave is the angular wave number.

[0115] (5) Within a scale range excluding the lowest frequency macroscopic shape and noise close to the Nyquist frequency, the relationship between power spectral density and wavenumber in a double logarithmic coordinate system can be expressed as:

[0116]

[0117] In the formula, β is the power spectral index, which is obtained by fitting the relationship between logP and logk using linear regression.

[0118] (6) Finally, the profile is adopted only when the goodness-of-fit R² meets the preset requirements. For a one-dimensional self-affine profile, the fractal dimension of the surface profile is calculated by the following formula:

[0119]

[0120] Step 202: Calculate the fractal dimension of multiple profiles at the same measurement moment, and use the statistically representative value as the fractal wear state D at that moment. t And record the standard deviation. This yields the historical state sequence {(E} for each honing wheel. t D t )}.

[0121] The average trend of fractal wear state with cumulative machining amount is fitted based on data from multiple independent life cycles. For working conditions with an initial increase and a later decrease, the following formula can be used:

[0122]

[0123] Where u=[n,f z ,f x ,d], and constrain c1(u)>0, c2(u)>0, α2>α1>0.

[0124] c1(u) and c2(u) can be represented using low-order response surfaces that include main effects and necessary interaction terms. If the experimental data do not support a double power-law form, piecewise monotonic splines or a generalized additive model with inflection points can be used. This trend model is a statistical degradation model and should not be expressed as a rigorous physical equation in the absence of mechanistic derivation.

[0125] Step 3: Construct the fractal dimension time-series Transformer prediction model. In Step 3, the fractal dimension time-series Transformer prediction model is constructed. The flowchart is as follows: Figure 3 As shown, specifically:

[0126] Step 301: Define model input and output: The model input includes the historical fractal states up to the current time [D1,…,D…]. t ], corresponding cumulative processing volume [E1,…,E t The model output includes batch parameters such as process parameters (u), honing wheel abrasive particle size, and binder type. The model output also includes the fractal dimension sequence for future machining stages, as well as tooth surface quality indicators or the probability of quality deviations.

[0127] Step 302: Design the model structure, employing a two-layer Transformer encoder as an implementation method. First, through the input embedding layer, the historical fractal dimension, cumulative number of processed parts, and process parameters are mapped into a 64-dimensional feature vector, which is then fused with the positional encoding of the number of processed parts to form temporal input features. A multi-head self-attention layer is used, with two layers of multi-head self-attention, each with eight attention heads, to capture the long-range dependencies between different wear stages and identify wear acceleration abrupt change points. Secondly, an adaptive weight module for life stages is configured, dividing the honing wheel life into three stages: initial, middle, and late. During training, late-stage samples are assigned a 1.5-fold dynamic weight to improve the prediction accuracy for the later stages of life.

[0128] A trend constraint term is set, incorporating the fractal dimension degradation trend model established in step 2 as a regularization term into the loss function to ensure the model output aligns with the known wear trend. Finally, a multi-task output layer is defined with two parallel fully connected branches. The main branch outputs the predicted fractal dimension value for future machining stages, while the auxiliary branch outputs tooth surface quality indicators or the probability of quality deviation. The tooth surface quality indicators include surface roughness, total tooth profile deviation, tooth profile shape deviation, total tooth direction deviation, and cumulative total tooth pitch deviation. This achieves joint modeling of honing wheel wear state prediction and tooth surface quality early warning.

[0129] Step 303: Design of joint loss function:

[0130]

[0131] In the formula, L MSE L is the mean square error of the fractal dimension prediction. TRE To account for the consistency error between the predicted trajectory and the statistical degradation model, L QUA λ1 and λ2 are the tooth surface quality prediction error and the balance coefficients.

[0132] The dataset is grouped by complete honing wheel or complete dressing cycle, and the test set must not contain adjacent measurement points of the same honing wheel from the training set. The model evaluation should at least report the MAE, threshold crossover time error, and remaining lifetime relative error, and compare it with unconstrained models and commonly used sequence models.

[0133] Step 304: Model Training and Incremental Update. First, the dataset is divided using time-series cross-validation, with a 7:1.5:1.5 ratio for training, validation, and test sets to avoid leakage of time-series information. Then, the training parameters are set using the AdamW optimizer with an initial learning rate of 0.001, decaying by 10% every 10 epochs, a batch size of 8, and 100 training epochs. An early stopping strategy is implemented, stopping the training if the validation set loss does not decrease for three consecutive epochs. Finally, incremental training is performed, updating only the model's attention weights and output layer parameters every 10 batches of new experimental data, thus shortening the training time and adapting to process adjustment requirements.

[0134] From the above steps, we can obtain Figure 4 and Figure 5 The chart shown compares the predicted values ​​with the actual values.

[0135] Step 4: Calculation of Remaining Life and Determination of Repair Timing. Step 4, specifically the calculation of remaining life and determination of repair timing, involves:

[0136] Step 401: Construct a dataset corresponding to the fractal dimension and the probability of out-of-tolerance tooth surface quality. Align the fractal dimension of the honing wheel imprint profile obtained at different processing stages in Step 1 with the tooth surface quality detection results of the gears processed at the corresponding stages. The tooth surface quality detection result is the surface roughness. Let Q be the tooth surface quality index of the i-th sampling stage. i The corresponding allowable tolerance limit is Q. lim A quality deviation label y is defined as 0.3 when at least one tooth surface quality index exceeds its allowable tolerance limit. i =1, otherwise define y i =0.

[0137] Construct the out-of-range probability input feature vector for the i-th sampling stage , where D i The fractal dimension of the current processing stage. This represents the change in fractal dimension between adjacent sampling stages. E represents the rate of degeneration of the fractal dimension. i n represents the number of parts already processed. i f z,i f x,i d i These are the spindle speed, axial feed rate, radial feed rate, and number of sparkless honing operations, respectively. i This refers to batch-level parameters in honing wheel material, abrasive particle size, binder type, and workpiece material.

[0138] Step 402: Establish a tooth surface quality deviation probability model. Input the deviation probability into the feature vector X. i As input, use the quality out-of-tolerance label y i To establish the output, a mapping relationship is established between the fractal dimension and the probability of out-of-tolerance tooth surface quality. The probability of out-of-tolerance quality is calculated using a logistic regression model.

[0139]

[0140] Where, p i Let be the probability that the tooth surface quality deviates from the acceptable range during the i-th machining stage. For the intercept term, These are the parameters to be trained. The model parameters are obtained through training using the cross-entropy loss function.

[0141] Step 403: Calculate the remaining number of workpieces to be processed by the honing wheel. At the current processing stage t, use the time-series prediction model established in Step 3 to predict the fractal dimension sequence for several future processing stages:

[0142]

[0143] By combining the corresponding process parameters with the quality deviation probability model established in step 4.2, the quality deviation probability sequence for each future processing stage is obtained:

[0144]

[0145] Set the allowable quality deviation probability threshold to p lim Set to 0.5, when a certain number of processed parts E in the future t+s satisfy When this number of processed parts is determined, it is set as the early warning point for the honing wheel's life or the end point of its quality constraint life.

[0146] The remaining number of workpieces (RUL) for the honing wheel is calculated using the following formula:

[0147]

[0148] Among them, E t E represents the current number of parts processed. t+s This is the predicted number of processed parts that will reach the probability threshold for the first time due to quality deviation.

[0149] Step 404: Establish the decision objective for repair timing. To determine the repair timing, a comprehensive expected cost function is further established, which includes repair costs, downtime costs, and quality loss costs.

[0150] Assume the timing for the repair to be evaluated is after processing h more parts from the current stage. The fixed repair cost is C. r Set to 500, unit downtime cost C s Set at 150 yuan / hour, with a single downtime of T. r The time is set to 0.4 hours, and the cost of quality loss due to scrapping or rework of a single workpiece is C. q If the price is set to 100 yuan, the probability of the quality of the s-th workpiece being out of tolerance in the future is: The unit effective processing cost corresponding to the repair timing h to be evaluated can be expressed as:

[0151]

[0152] in, Set to 10 -6 To prevent extremely small positive numbers with a denominator of zero. max Setting it to 0.7 satisfies the probability constraint of quality deviation. Among the adjustment opportunities to be evaluated, select the one that makes J( h The minimum h is taken as the optimal number of delayed processing parts, that is, Therefore, the optimal timing for repair, considering both the lowest overall cost and the required quality, is:

[0153]

[0154] Where E* represents the recommended number of workpieces for honing wheel dressing. Thus, under the premise of ensuring that the probability of tooth surface quality deviation is controlled, a quantitative decision on the timing of honing wheel dressing is achieved by comprehensively considering dressing costs, downtime costs, and quality deviation losses.

[0155] Based on the above steps, the recommended honing wheel dressing time is 67 times, and the honing wheel life warning time is 74 times. Figure 6 As shown.

Claims

1. A method for characterizing the wear state and predicting the remaining life of a honing wheel for high-power gear honing, characterized in that, Includes the following steps: S1) Honing wheel positioning, imprinting and contour data acquisition; establish tooth number marks on the honing wheel, and use tooth direction and axial positioning references to define the effective contact area as the repeated measurement area; before processing and after processing a preset number of workpieces, stop the machine, use vinyl polysiloxane material to imprint the repeated measurement area, after the imprint sample is cured, use a laser profilometer to obtain multiple two-dimensional contour curves, and record the number of processed parts and measurement conditions; S2) Contour fractal dimension calculation and degradation trend modeling: The collected contour curves are sequentially detrended, filtered, and effective region truncation processed. The power spectrum method is used to calculate the fractal dimension of each contour. The statistical representative value of the fractal dimension of multiple contours at the same measurement time is taken as the fractal wear state at that time, thereby obtaining the historical state sequence of the honing wheel. Based on the historical state sequence under multiple process conditions, a degradation trend model of the fractal dimension changing with the cumulative number of processed parts is established. S3) Construct a fractal dimension time series prediction model; take the historical fractal dimension sequence, the cumulative number of processed parts sequence and process parameters as input, and add the degradation trend model established in step S2) as a constraint term into the loss function to train the time series prediction model to predict the fractal dimension change and the probability of tooth surface quality deviation in the future processing stage. S4) Calculate remaining life and determine the timing of overhaul; align the fractal dimension of different processing stages with the corresponding workpiece tooth surface quality inspection results in time to establish a mapping relationship between fractal wear state and tooth surface quality deviation probability; calculate the tooth surface quality deviation probability of each future processing stage based on the future fractal dimension sequence predicted in step S3); when the deviation probability reaches the preset threshold for the first time, determine the honing wheel life warning point and calculate the number of remaining processed parts; combine overhaul cost, downtime cost and quality loss cost to determine the overhaul timing with the lowest overall cost.

2. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 1, characterized in that, Step S1) specifically includes the following sub-steps: S1.1) An experimental matrix is ​​constructed using a central composite design, covering the range of commonly used process parameters in actual production; the process parameters include spindle speed, axial feed rate, radial feed rate, and number of sparkless honing operations; each process combination completes a full dressing cycle of a preset number of gears; S1.2) After processing a preset number of workpieces, stop the machine and use vinyl polysiloxane material to make a rubbing under the same positioning conditions, and record the material type, curing time, ambient temperature, contact pressure and repeat positioning error; use a laser profilometer to scan the rubbing sample and extract no less than 5 parallel contour curves in each positioning area. S1.3) Redundant data in non-contact areas are removed, median filtering is used to remove scanning noise, and the installation tilt error is eliminated by fitting the baseline using the least squares method to obtain standardized contour height data.

3. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 1, characterized in that, Step S2) specifically includes the following sub-steps: S2.1) The fractal dimension D is calculated using the power spectrum method; the standardized contour height data is detrended to eliminate the influence of macroscopic shape on the spectral analysis; the detrended data is subjected to discrete Fourier transform to calculate the power spectral density; the frequency index is converted into spatial frequency and angular wavenumber; within a scale range excluding the lowest frequency macroscopic shape and noise close to the Nyquist frequency, the relationship between the power spectral density and wavenumber is fitted by linear regression in a double logarithmic coordinate system to obtain the power spectral index β; the contour is used only when the goodness of fit R² meets the preset requirements, and the fractal dimension D is calculated by the following formula: . S2.2) Calculate the fractal dimension for multiple profiles at the same measurement time, and use the mean, median, or truncated mean as the statistical representative value, and record the standard deviation, thereby constructing the historical state sequence of the honing wheel. ; S2.3) Based on data from multiple independent life cycles, a degradation trend model of the fractal dimension as a function of the cumulative number of processed parts is established. For working conditions with an initial increase and a later decrease, the following double power law form is adopted: In the formula, u=[n,f z ,f x [d] represents the process parameter vector, D0 is the initial fractal dimension, c1(u) and c2(u) are coefficients related to the process parameters, α1 and α2 are power-law exponents, and are constrained to have c1(u)>0, c2(u)>0, and α2>α1>0; c1(u) and c2(u) are represented by low-order response surfaces containing main effects and necessary interaction terms; when the experimental data do not support the double power-law form, piecewise monotonic splines or generalized additive models with inflection points are used instead.

4. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 1, characterized in that, Step S3) specifically includes the following sub-steps: S3.1) Define the model input and output; the model input includes the historical fractal state sequence up to the current moment. Corresponding cumulative processing volume Process parameters The model output includes batch parameters such as the abrasive grain size and bond type of the honing wheel; the model output includes the fractal dimension sequence and tooth surface quality index or the probability of quality deviation in the future processing stage; S3.2) Design the model structure; the time-series prediction model adopts the Transformer encoder architecture; the historical fractal dimension, cumulative number of processed parts and process parameters are mapped into multi-dimensional feature vectors through the input embedding layer, and fused with the position encoding of the number of processed parts to form time-series input features; A multi-layer, multi-head self-attention mechanism is adopted to capture the long-range dependency between different wear stages; an adaptive weight module for life stage is set up to divide the honing wheel life into three stages: early, middle and late, and higher dynamic weights are assigned to late samples during training; a multi-task output layer is set up, with the main branch outputting the fractal dimension prediction value of the future processing stage and the auxiliary branch outputting the tooth surface quality index or the probability of quality deviation. S3.3) Design the joint loss function; the joint loss function of the time series prediction model is: in, The mean square error of the fractal dimension prediction. To account for the consistency error between the predicted trajectory and the statistical degradation model, This is the prediction error for tooth surface quality. , The balance coefficient is used; the dataset is divided into groups according to a complete honing wheel or a complete dressing cycle, and the test set must not contain adjacent test points of the same honing wheel in the training set; S3.4) Training and updating of time series prediction models.

5. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 4, characterized in that, The training and updating method of the time series prediction model is as follows: time series cross-validation is used to divide the training set, validation set and test set to avoid leakage of time series information; AdamW optimizer is used for training and an early stopping strategy is implemented; after each preset batch of new experimental data is accumulated, only the attention weights and output layer parameters of the model are updated to achieve incremental training and adapt to the process adjustment requirements.

6. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 1, characterized in that, Step S4) specifically includes the following sub-steps: S4.1) Construct the out-of-range probability input feature vector ,in The fractal dimension of the current processing stage. This represents the change in fractal dimension between adjacent sampling stages. The rate of fractal dimension degradation. This represents the number of parts already processed. For batch-level parameters in honing wheel material, abrasive grain size, binder type, and workpiece material; a logistic regression model is used to establish the probability of quality deviation: The model parameters are obtained through training using the cross-entropy loss function; S4.2) In the current processing stage The time series prediction model established in step S3) is used to predict the future fractal dimension sequence. By combining the quality deviation probability model established with the corresponding process parameters input in S4.1, the quality deviation probability sequence for each future processing stage is obtained. Determine the lifespan warning point; S4.3) Establish the expected comprehensive cost function that includes repair costs, downtime costs, and quality loss costs; assume that processing continues from the current stage. After finishing, the unit effective processing cost is: in, To fix repair costs, Cost per unit downtime This refers to the downtime for a single maintenance operation. Cost per unit of quality loss To prevent extremely small positive numbers with a denominator of zero; when satisfying ( Under the constraints of ), take smallest Therefore, the recommended number of parts to be processed at the appropriate repair time is: .

7. The method for characterizing the wear state and predicting the remaining life of a high-power honing grinding wheel according to claim 6, characterized in that, The number of remaining processed parts is calculated using the following formula: in, This represents the current number of pieces processed. For the first time in the predicted quality out-of-range probability sequence to satisfy The corresponding number of processed parts at that time This is the preset threshold for the probability of quality deviation.

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