Dynamic modeling method for surface topography of camshaft non-circular profile high-speed grinding

Abstract

The present application relates to the field of machining modeling, in particular to a camshaft non-circular contour high-speed grinding surface morphology dynamic modeling method, which comprises: collecting a mixed signal to obtain a source signal component corresponding to the grinding wheel wear; selecting a signal feature with high correlation with the grinding wheel wear to combine the grinding wheel abrasive wear area to construct an abrasive wear online prediction model based on FAW-DELM; measuring the grinding wheel surface morphology, setting the abrasive blade height to obey the normal distribution, calculating the grinding wheel abrasive blade height through the real-time grinding wheel abrasive wear area, dynamically adjusting the mean value of the normal distribution, combining the calculation results of the measured abrasive space distribution to establish a grinding wheel surface morphology dynamic simulation model; establishing a single abrasive particle grinding motion trajectory equation considering vibration; combining the grinding wheel surface morphology dynamic simulation model and the single abrasive particle grinding motion trajectory equation considering vibration to generate the grinding surface morphology. It can be dynamically analyzed and has high accuracy.

Description

Technical Field

[0001] This invention relates to the field of machining modeling technology, and in particular to a dynamic modeling method for the surface morphology of a non-circular profile camshaft during high-speed grinding. Background Technology

[0002] The camshaft is a key component of an engine, and the quality of its working surface is a core factor affecting engine efficiency and service life. High-speed grinding, as the final process for the non-circular contour surface of the camshaft, determines the quality of its working surface.

[0003] The primary purpose of high-speed grinding is to improve dimensional accuracy and surface quality, with surface roughness being a crucial parameter. Although the material removal mechanism in high-speed grinding is complex and involves multiple factors that significantly influence the final surface roughness, previously, multiple rounds of testing were often required to determine the ideal surface roughness to guide the optimization of machining parameters. However, with the development of digital and intelligent technologies, simulation modeling can be used to simulate the surface morphology of the machined surface. Based on the obtained surface morphology, the surface roughness can be calculated, which has become an important method for optimizing machining parameters. However, current surface morphology modeling methods are static. In actual grinding, wheel wear and vibration are constantly present, both of which significantly affect the surface morphology and, consequently, surface roughness. Furthermore, wheel wear occurs in real-time during the grinding process and its condition changes dynamically as grinding continues. It is difficult to know the real-time wear status of the wheel during grinding. These factors make it difficult to dynamically model the surface morphology of non-circular profile camshafts in high-speed grinding using existing technologies, hindering the accurate guidance of machining parameter optimization through modeling. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic modeling method for the surface morphology of camshafts with non-circular contours during high-speed grinding, aiming to solve the problem in the prior art that it is difficult to dynamically model the surface morphology of camshafts with non-circular contours during high-speed grinding.

[0005] To achieve the above objectives, this invention provides a dynamic modeling method for the surface morphology of high-speed grinding of non-circular profile camshafts, comprising the following steps: S1. Acquiring mixed signals during the high-speed grinding process of non-circular profile camshafts using acoustic emission sensors and vibration sensors, preprocessing and separating the mixed signals to obtain source signal components corresponding to grinding wheel wear; S2. Extracting time-domain and frequency-domain signal features from the source signal components, selecting signal features highly correlated with grinding wheel wear, and combining them with the grinding wheel abrasive wear area to construct an online abrasive wear prediction model based on FAW-DELM, predicting the real-time grinding wheel abrasive wear area through real-time source signal components, wherein FAW-DELM is a parameter optimization method using the fireworks algorithm to optimize the input layer weights and offset thresholds of a deep extreme learning machine; S3. Measure the surface morphology of the grinding wheel, using a triangular pyramid to simulate the shape of the abrasive grains. Set the abrasive grain protrusion height to follow a normal distribution, where the mean of the normal distribution represents the abrasive grain protrusion height and the variance represents the abrasive grain distribution. As the grinding wheel wears, the protrusion height decreases but the distribution remains constant. Calculate the abrasive grain protrusion height using the real-time abrasive grain wear area obtained in step S2, dynamically adjust the mean of the normal distribution, and obtain a dynamic normal distribution model of the abrasive grain protrusion height. Combine this with the spatial distribution calculation results of the abrasive grains obtained when measuring the surface morphology of the grinding wheel to establish a dynamic simulation model of the grinding wheel surface morphology; S4 Based on the grinding parameters and the motion relationship of the XC-axis linkage grinding of the camshaft, the motion trajectory equation of a single abrasive grain is established; the radial vibration of the grinding wheel along the X direction is simplified to simple harmonic motion, and radial vibration is introduced into the motion trajectory equation of a single abrasive grain to obtain the motion trajectory equation of a single abrasive grain considering vibration; S5. Combining the dynamic simulation model of the grinding wheel surface morphology and the motion trajectory equation of a single abrasive grain considering vibration, the grinding surface morphology is generated by superimposing multiple abrasive grain trajectories, using interference and envelope algorithms, and the surface roughness is calculated using the surface morphology data.

[0006] Furthermore, in step S1, the preprocessing includes an outlier detection and optimization process: First, the original signal is divided into multiple signal segments; then, the signal segments are further divided into several signal parts. If the root mean square value of a certain signal part exceeds a set threshold, the signal part is considered an outlier. The threshold is derived based on the 3σ principle; finally, the outliers are removed from the original signal and the data is supplemented by linear interpolation.

[0007] Further, in step S1, blind source separation employs a signal processing method based on WPD-EWT-FastICA, which includes: processing the acoustic emission signal using the WPD-FastICA method with a sampling frequency of 1MHz, performing three-level decomposition using wavelet packet decomposition, selecting the db10 wavelet as the wavelet basis function, constructing an input matrix from the frequency band node signal with the highest energy proportion from the decomposed node signal, and separating the independent components using the FastICA algorithm; processing the vibration signal using the EWT-FastICA method with a sampling frequency of 6400Hz, performing decomposition using empirical wavelet transform, adaptively segmenting the Fourier spectrum of the signal, determining the frequency band boundary based on the spectral maxima, constructing an empirical wavelet filter bank, constructing an input matrix from the decomposed components, and separating the independent components using the FastICA algorithm.

[0008] Furthermore, in step S2, the signal features that are highly correlated with grinding wheel wear include the root mean square value of the acoustic emission signal, the centroid frequency of the acoustic emission signal, the root mean square value of the vibration signal, the variance of the vibration signal, the skewness of the vibration signal, and the centroid frequency of the vibration signal.

[0009] Furthermore, in step S2, the population size of the fireworks algorithm is set to 100, and the maximum number of iterations is 100; the deep limit learning machine is a 3-layer deep structure with 60 input neurons in each layer and the activation function of the hidden layer is Sigmoid.

[0010] Furthermore, in step S3, the dynamic normal distribution model of the abrasive grain exit height is:

[0011] ,

[0012] In the formula, H g The abrasive grain exit height is represented by σ; σ represents the variance of the normal distribution, σ = (D max -D min ) / 8;D max D represents the maximum height of the abrasive grain exiting the cutting edge. min The minimum abrasive grain protrusion height is represented by the values ​​measured during the morphology measurement of the grinding wheel surface; ψ represents the apex angle of the triangular pyramid; S w (t) represents the wear area of ​​the grinding wheel abrasive grains at the previous moment.

[0013] Furthermore, in step S4, the method for establishing the motion trajectory equation of a single abrasive grain grinding is as follows: using the roller tappet model, the relationship between the displacement of the grinding wheel center O2 along the X direction and the rotation angle θ of the roller center O1 is obtained as follows:

[0014] ,

[0015] In the formula, O is the cam center; O1 is the roller center; H(θ) is the relationship between the lift H and the rotation angle θ in the cam lift table; r g r is the roller radius; s r is the radius of the grinding wheel. j Let be the base circle radius of the cam; the relationship between the cam rotation angle α and the rotation angle θ of the roller center O1 is:

[0016] ;

[0017] The cam's rectangular coordinates (x, y) are converted to polar coordinates (ρ, φ) from 0 to 2π, as shown in the following formula:

[0018] ;

[0019] The XC axis displacement and rotation table can be obtained from the polar coordinate equation, and the formula is as follows:

[0020] ,

[0021] In the formula, S x C is the distance between the grinding wheel center O2 and the cam center O; C is the cam rotation angle in polar coordinates. ; Based on the formula:

[0022] ,

[0023] In the formula, S x (t) is the real-time distance between the grinding wheel center O2 and the cam center O; then:

[0024] ,

[0025] In the formula, X S (t) and Y S (t) represents the real-time coordinate of the grinding wheel center O2; C(t) represents the real-time polar coordinate rotation angle of the cam, C(t) = ωt, where ω is the angular velocity of the cam; the coordinates of the abrasive grain globally are the superposition of the real-time coordinates of the grinding wheel center O2 and the motion of the abrasive grain in the grinding wheel coordinate system. Let the polar coordinates of the abrasive grain at the grinding wheel center O2 be (r s , θ s (t)), θ s (t)= ω s t, ω s Given the angular velocity of the grinding wheel, the equation for the grinding trajectory of a single abrasive grain can be obtained:

[0026] ,

[0027] In the formula, x g (t) and y g (t) represents the real-time coordinates of the abrasive grain.

[0028] Furthermore, in step S4, the mathematical model for the radial vibration of the grinding wheel introduced when establishing the equation for the grinding motion trajectory of a single abrasive grain considering vibration is as follows:

[0029] ,

[0030] In the formula, W k ξ represents the amplitude of the grinding wheel vibration; k The initial phase of the grinding wheel vibration signal is set to 0. =ω s ; ,set up = 1 × 10 -12 m⋅s 2 / rad 2 By incorporating the mathematical model of radial vibration of the grinding wheel into the single-grain grinding motion trajectory equation, the single-grain grinding motion trajectory equation considering vibration is obtained as follows:

[0031] ;

[0032] Let two adjacent abrasive grains be i and j, and the initial angle difference between the two adjacent abrasive grains be... Then we have:

[0033] ;

[0034] ;

[0035] The trajectory difference between two adjacent abrasive grains is:

[0036] ;

[0037] The spacing between two adjacent abrasive grains is:

[0038] .

[0039] Further, step S5 includes: S51. Discretizing the surface of the grinding wheel and the non-circular contour surface of the camshaft; S52. Selecting an axial section of the grinding wheel, extracting its abrasive data, calculating its trajectory and storing it in matrix W(i, j); cyclically iterating through all axial sections until the trajectory of all abrasive grains is covered; S53. When multiple abrasive grain trajectories intersect to form an intersection point, if the height value of the subsequent trajectory at the intersection point is lower, then the lower point is updated as an effective interference point, the lowest point z(m, n) of all trajectories is selected and the matrix W(i, j) is updated to form the workpiece surface contour; S54. Extracting data points that satisfy the surface morphology generation principle from the matrix W(i, j), storing them in matrix Wz(i, j), and generating the grinding surface morphology through an envelope algorithm.

[0040] This invention provides a dynamic modeling method for the surface morphology of non-circular profile high-speed grinding of camshafts. Compared with existing technologies, it first separates the mixed signal to obtain the source signal component corresponding to the grinding wheel wear, and obtains the real-time grinding wheel abrasive wear area through an online abrasive wear prediction model. Using the real-time grinding wheel abrasive wear area combined with the spatial distribution calculation results of abrasive grains obtained from measuring the grinding wheel surface morphology, a dynamic simulation model of the grinding wheel surface morphology is established to solve the problem of difficulty in knowing the real-time wear condition of the grinding wheel in existing technologies. Then, vibration factors are incorporated, and a single abrasive grain grinding motion trajectory equation considering vibration is proposed, making the simulation results closer to reality. By combining the dynamic simulation model of the grinding wheel surface morphology and the single abrasive grain grinding motion trajectory equation considering vibration, it can effectively simulate the continuous wear of the grinding wheel during the grinding process and the influence of vibration on the grinding surface morphology, realizing dynamic modeling of the grinding surface morphology. Verification shows that this method has high simulation accuracy and can provide more accurate guidance for optimizing machining process parameters. Attached Figure Description

[0041] Figure 1 This is a flowchart of a signal processing method based on WPD-EWT-FastICA;

[0042] Figure 2 This is a flowchart of FAW-DELM;

[0043] Figure 3 These are prediction results from the training set of the online prediction model for abrasive wear based on FAW-DELM;

[0044] Figure 4 These are the test set prediction results of the online prediction model for abrasive wear based on FAW-DELM;

[0045] Figure 5 This is a dynamic simulation diagram of the surface morphology of the grinding wheel in this embodiment;

[0046] Figure 6 This is a schematic diagram of a roller tappet model;

[0047] Figure 7 This is a logical framework diagram of the dynamic modeling method for surface morphology of high-speed grinding of non-circular profile camshaft according to the present invention;

[0048] Figure 8 These are comparison images of the surface morphology of the camshaft during high-speed grinding and the simulated surface morphology.

[0049] Figure 9 These are the measured and predicted values ​​of the surface roughness of the base circle portion of the camshaft. Detailed Implementation

[0050] The embodiments of the present invention will be described in detail below.

[0051] This invention provides a dynamic modeling method for the surface morphology of a non-circular profile camshaft during high-speed grinding, comprising the following steps: S1. Acquiring mixed signals during the high-speed grinding process of a non-circular profile camshaft using acoustic emission sensors and vibration sensors, preprocessing the mixed signals and performing blind source separation to obtain source signal components corresponding to grinding wheel wear; S2. Extracting time-domain and frequency-domain signal features from the source signal components, selecting signal features highly correlated with grinding wheel wear, and combining them with the grinding wheel abrasive wear area to construct a model based on FAW-DELM. An online prediction model for abrasive wear is developed, which predicts the real-time abrasive wear area of ​​the grinding wheel through real-time source signal components. FAW-DELM optimizes the input layer weights and offset thresholds of the deep extreme learning machine using the fireworks algorithm. S3. The surface morphology of the grinding wheel is measured, and the abrasive grain shape is simulated using a triangular pyramid. The abrasive grain protrusion height is set to follow a normal distribution, where the mean of the normal distribution represents the abrasive grain protrusion height, and the variance represents the abrasive grain distribution. The distribution remains unchanged even as the grinding wheel wear protrusion height decreases. The abrasive grain protrusion height is calculated using the real-time abrasive wear area obtained in step S2. The mean of the normal distribution is dynamically adjusted to obtain a dynamic normal distribution model for the abrasive grain protrusion height. This model is then combined with measurement... S4. Based on the spatial distribution calculation results of abrasive grains obtained from the grinding wheel surface morphology analysis, a dynamic simulation model of the grinding wheel surface morphology is established; S5. Based on the grinding parameters and the motion relationship of the camshaft XC axis linkage grinding, the single abrasive grain grinding motion trajectory equation is established; the radial vibration of the grinding wheel along the X direction is simplified to simple harmonic motion, and radial vibration is introduced into the single abrasive grain grinding motion trajectory equation to obtain a single abrasive grain grinding motion trajectory equation considering vibration; S6. Combining the dynamic simulation model of the grinding wheel surface morphology and the single abrasive grain grinding motion trajectory equation considering vibration, the grinding surface morphology is generated through the superposition of multiple abrasive grain trajectories, interference and envelope algorithms, and the surface roughness is calculated using the surface morphology data.

[0052] Based on the above-described method steps, this dynamic modeling method for the surface morphology of high-speed grinding of non-circular profile camshafts first separates the mixed signals to obtain the source signal components corresponding to the grinding wheel wear. Then, it obtains the real-time grinding wheel abrasive wear area through an online abrasive wear prediction model. Using the real-time grinding wheel abrasive wear area combined with the spatial distribution calculation results of abrasive grains obtained when measuring the grinding wheel surface morphology, a dynamic simulation model of the grinding wheel surface morphology is established to solve the problem of difficulty in knowing the real-time wear condition of the grinding wheel in existing technologies. Next, vibration factors are incorporated, and a single abrasive grain grinding motion trajectory equation considering vibration is proposed, making the simulation results closer to reality. By combining the dynamic simulation model of the grinding wheel surface morphology and the single abrasive grain grinding motion trajectory equation considering vibration, the method can effectively simulate the continuous wear of the grinding wheel during the grinding process and the influence of vibration on the grinding surface morphology, achieving dynamic modeling of the grinding surface morphology and providing more accurate guidance for optimizing machining process parameters.

[0053] The steps in this method will be explained in further detail below.

[0054] In this embodiment, the acoustic emission data acquisition platform uses a W800 acoustic emission sensor and a PAS preamplifier with a frequency bandwidth of 50~800 kHz. The preamplifier ratio is set to 40 dB, and the filtering frequency band is 20~1200 kHz. The acquisition card used is the USB-6351 from NI (National Instruments). The attenuation of the acoustic emission signal is mainly affected by the propagation distance. Therefore, the acoustic emission sensor needs to be installed as close as possible to the grinding area without interfering with the grinding process. In this embodiment, the acoustic emission sensor is installed in the Y-axis direction of the grinding machine tailstock, and the acoustic emission signal sampling frequency is set to 1 MHz. The vibration signal data acquisition platform uses the ECON vibration data acquisition system. In order to obtain accurate vibration state information during the grinding process, the vibration sensor is installed in the X-axis direction of the headstock. The vibration frequency of grinding is mainly concentrated in the range of 0~3000 Hz, so the acquisition frequency is set to 6400 Hz.

[0055] In the complex environment of high-speed grinding of non-circular camshaft profiles, sensor signal acquisition may result in the collection of some abnormal signals, which will adversely affect the monitoring of the grinding process. Therefore, a statistical method is constructed to detect and delete outliers while retaining normal signals. In this embodiment, in step S1, the preprocessing includes an outlier detection and optimization process: First, the original signal is divided into multiple signal segments; then, the signal segments are further divided into several signal parts. If the root mean square value of a certain signal part exceeds a set threshold, the signal part is considered an outlier. The threshold is derived based on the 3σ principle; finally, the outliers are deleted from the original signal and the data is supplemented by linear interpolation.

[0056] according to In principle, the threshold is derived from the following formula: Among them, T p The threshold representing the root mean square of the p-part signal; μ p and σ p These represent the average and standard deviation of all signals preceding p in a given signal segment. After removing outliers from the vibration and acoustic emission data, linear interpolation is used to supplement the data and ensure continuity in the time dimension. Simultaneously, wavelet threshold denoising is applied to further improve the signal-to-noise ratio, filtering out interference signals to make the signal carrying useful information clearer.

[0057] When a grinding wheel is processed under different wear conditions, it will inevitably emit different vibration and acoustic emission signals. Conversely, by obtaining these signals during real-time processing, the wear state of the grinding wheel can be determined, provided that the source signal component corresponding to the grinding wheel wear can be extracted. The vibration and acoustic emission signals collected by sensors during the grinding process are actually the combined effect of multiple "sources" on the entire system, and the source signals and mixing methods are difficult to predict. Blind source separation methods can separate the required target components from sensor data, but the number of sensors must be no less than the number of signal sources. However, it is difficult to install a large number of sensors in a grinding system. Therefore, a signal decomposition method can be used to divide the sensor signal into multiple components, and then the blind source separation technology can be used to separate each source signal. Only after separating the vibration source signal component corresponding to the grinding wheel wear can it be used for subsequent processing. Therefore, this embodiment considers the high-speed grinding process of a non-circular profile camshaft and proposes a signal separation method based on WPD-EWT-FastICA.

[0058] In this embodiment, in step S1, as follows Figure 1 As shown, blind source separation employs a signal processing method based on WPD-EWT-FastICA, which includes: processing the acoustic emission signal using the WPD-FastICA method with a sampling frequency of 1MHz; performing three-level decomposition using wavelet packet decomposition with the db10 wavelet as the wavelet basis function; selecting the frequency band node signal with the highest energy proportion from the decomposed node signals to construct the input matrix; and separating the independent components using the FastICA algorithm. Analysis shows that the acoustic emission source signal component corresponding to grinding wheel wear is located in the independent component IC2. For the vibration signal, the EWT-FastICA method is used with a sampling frequency of 6400Hz. Empirical wavelet transform is used for decomposition, adaptive segmentation of the Fourier spectrum is performed, frequency band boundaries are determined based on spectral maxima, an empirical wavelet filter bank is constructed, and the decomposed components are used to construct the input matrix. The independent components are then separated using the FastICA algorithm. Analysis shows that the vibration source signal component corresponding to grinding wheel wear is located in the independent component IC4.

[0059] For the preprocessed and separated acoustic emission and vibration signals, statistical methods are used to extract signal features and construct the input matrix of the online abrasive wear prediction model to dynamically describe the abrasive wear state of the grinding wheel during the grinding process. The quality of the signal features plays a crucial role in the model's prediction results; low correlation and high redundancy will degrade the performance of the prediction model. Therefore, correlation analysis of the signal features is conducted. Statistical feature calculations of the decomposed time-domain signals can typically describe the variation law of grinding wheel wear; similarly, frequency distribution can reflect the changes in the state of the grinding process. Therefore, in addition to time-domain feature calculations, corresponding features are also extracted in the frequency domain. Grinding wheel wear is usually a gradual and monotonically increasing process, but the relationship between the wear rate and the vibration and acoustic emission signal features is not necessarily linear. To improve the model's generalization ability, Spearman correlation analysis is used to select signal features with high correlation to the grinding wheel wear state as the input feature matrix of the prediction model. Spearman correlation data with a value between 0.6 and 0.79 are generally considered to be strongly correlated, while those between 0.8 and 1.00 are considered extremely strongly correlated. Correlation analysis was performed on the extracted signal features and grinding wheel wear. Finally, six signal features with strong correlation to grinding wheel wear were selected: root mean square value of acoustic emission signal (AE-RMS), root mean square value of vibration signal (V-RMS), variance of vibration signal (V-STD), skewness of vibration signal (VS), centroid frequency of acoustic emission signal (AE-FC), and centroid frequency of vibration signal (V-FC). These features were then used to construct the input matrix T of the prediction model. S .

[0060] To obtain a dynamic data model of grinding wheel wear in subsequent grinding surface morphology modeling, a deep limit learning machine method optimized based on the fireworks algorithm was used to construct an online prediction model for the abrasive wear area of ​​the grinding wheel, with T... S The input matrix is ​​the abrasive wear area of ​​the grinding wheel, and the output matrix is ​​the abrasive wear area of ​​the grinding wheel, thus realizing the dynamic characterization of the abrasive wear area of ​​the grinding wheel.

[0061] The Fireworks algorithm (FWA) possesses strong global and local search capabilities. Deep Extreme Learning Machine (DELM) combines Extreme Learning Machine (ELM) with an autoencoder (AE) to form an Extreme Learning Machine Autoencoder (ELM-AE), and constructs a deep network structure by stacking multiple ELM-AE modules. Based on ELM, DELM uses multiple ELM-AEs for unsupervised pre-training. The entire DELM is initialized with the output weights of each layer's ELM-AE. By training layer by layer using the ELM-AEs, high-level features of the original data can be learned. In DELM, the output of an upper-layer ELM-AE is considered the input of the lower layer, and so on; finally, the DELM model training is completed by solving for the final output weights. However, the input layer weights and offsets are not updated during DELM training, which means the final result will be affected by random input weights and random offsets. To improve model performance, FAW (Fast-Write) is used to optimize the input layer weights and offset thresholds to mitigate these two influencing factors. The optimization process of FAW-DELM is as follows: Figure 2 As shown. In this embodiment, the population size of the fireworks algorithm is set to 100, and the maximum number of iterations is 100; the deep extreme learning machine is a 3-layer deep structure with 60 input neurons in each layer, and the activation function of the hidden layer is Sigmoid.

[0062] Before constructing the online prediction model for abrasive wear, actual grinding experiments were conducted. The experiments considered the influence of non-circular contour surfaces, vibration during the grinding process, and the impact of grinding wheel wear. Grinding surface morphology detection, roughness measurement, and sensor signal acquisition (vibration and acoustic emission signals) were performed on the cam tip, lift, base circle, and return stroke sections. The surface morphology of the grinding wheel was also detected (including the shape, tip height, and distribution of abrasive grains). After each grinding cycle, images of the grinding wheel surface at six observation points were processed to obtain the abrasive wear area and number of abrasive grains. Assuming the number of abrasive grains is n and the wear area of ​​a single abrasive grain is A, the wear state of the grinding wheel is characterized by the average wear area of ​​a single abrasive grain, as shown in the following formula:

[0063] .

[0064] The previously constructed TS and the abrasive wear area of ​​the grinding wheel are used to construct the input matrix R of the FAW-DELM regression model. Thirty-six groups are uniformly selected from different grinding wheel wear state intervals as the training set, and 16 groups as the test set. The prediction results of the training set and test set of the FAW-DELM-based online abrasive wear prediction model are as follows: Figure 3and Figure 4 As shown, the R of its training set 2 =0.99128, R value of the test set 2 =0.96943. This demonstrates that the model has high prediction accuracy.

[0065] Grinding wheels are composed of a large number of random abrasive grains, making it difficult to accurately express or calculate the specific size, dimensions, and other static parameters of any abrasive grain. Therefore, this embodiment will introduce the online abrasive wear prediction model based on FAW-DELM established above on the basis of conventional grinding wheel surface morphology modeling, and then establish a dynamic simulation model of grinding wheel surface morphology that considers real-time grinding wheel abrasive wear.

[0066] It is generally believed that the microscopic geometric parameters of abrasive grains follow a certain distribution law. By measuring the surface morphology of the grinding wheel using optical instruments, abrasive grain characteristics (such as grain shape, cutting edge height, and distribution) are defined, and a mathematical model of the abrasive grain characteristics is obtained, thus establishing a grinding wheel surface morphology model. Therefore, this embodiment uses a confocal microscope to observe CBN abrasive grains, finding that the grain shapes are roughly divided into four categories: spherical, conical, pyramidal, and truncated octahedral. The number of each shape is counted. To ensure that the grinding wheel surface morphology model is as close to reality as possible, this embodiment uses a triangular pyramid to simulate the shape of CBN abrasive grains and uses an equivalent diameter to represent the grain size.

[0067] Meanwhile, by measuring and statistically analyzing the abrasive grain exit height, it was found that the exit height of the abrasive grain follows a normal distribution, that is, the abrasive grain exit height H... g The distribution function is as follows:

[0068] ,

[0069] In the formula, H g The abrasive grain exit height is represented by μ; μ represents the mean of the normal distribution, μ=(D max +D min ) / 2; σ represents the variance of the normal distribution. The value of σ is selected according to the 3 "σ" criterion: σ = (D max -D min ) / 8;D max D represents the maximum height of the abrasive grain exiting the cutting edge. min The minimum value representing the abrasive grain protrusion height is measured when measuring the surface morphology of the grinding wheel.

[0070] Subtle changes in the surface morphology of the grinding wheel significantly affect the surface roughness and smoothness of the workpiece. However, research has found that the impact of grinding wheel wear on the edge height mainly lies in the mean of a normal distribution, with little effect on its variance. Considering that the distribution of abrasive edge height is a crucial factor influencing the surface morphology of the grinding wheel and is difficult to dynamically describe through theoretical modeling, and given that surface profile generation is based on the superposition of abrasive grain movement trajectories and edge heights, and that a normal distribution directly relates to the generation of the grinding wheel surface and directly affects the grinding surface morphology, grinding wheel wear must be considered when establishing a simulation model for grinding surface morphology. As grinding progresses, abrasive grains gradually wear, and the distribution of abrasive edge height changes dynamically. The μ value quantifies the concentration trend of abrasive grain height; as the grinding wheel wears, the μ value shifts towards the 0 coordinate. Therefore, the aforementioned online prediction model for abrasive grain wear based on FAW-DELM is compared with the H... g By combining the distribution function, the distribution of the abrasive grain exit height is dynamically adjusted to simulate the grinding wheel wear process.

[0071] Assume the wear area of ​​the grinding wheel is S. w Since the triangular pyramid in this embodiment simulates the shape of CBN abrasive grains, the relationship between the increased area and reduced height of abrasive wear can be derived:

[0072] ;

[0073] Among them, S w (t) represents the wear area of ​​the grinding wheel abrasive particles obtained based on the previous moment.

[0074] Further, we can obtain:

[0075]

[0076] Considering that the change in abrasive grain protrusion height due to grinding wheel wear is not instantaneous but a continuous, cumulative process, we can predict the surface morphology to be formed at the next grinding moment based on the grinding wheel wear state at the previous moment after grinding is completed. Ultimately, the dynamic normal distribution model of the abrasive grain protrusion height, characterizing the abrasive grain distribution, can be obtained as follows:

[0077] ,

[0078] In the formula, ψ represents the vertex angle of the triangular pyramid; S w (t) represents the wear area of ​​the grinding wheel abrasive grains at the previous moment.

[0079] Based on the above, and combining the existing technical definition of the rotational transformation matrix and angle difference around the X-axis, the abrasive grains of the grinding wheel are rotated and misaligned to obtain the spatial distribution calculation results of the abrasive grains. A dynamic simulation model of the grinding wheel surface morphology can be obtained through MATLAB programming and simulation. The simulation results are as follows: Figure 5 As shown.

[0080] The mathematical model of the grinding motion for non-circular profile camshafts is a crucial mathematical foundation for grinding surface morphology modeling; therefore, kinematic analysis of the high-speed grinding system for non-circular profile camshafts is necessary. During the grinding process, as the cam rotates through an angle, the grinding wheel head reciprocates along the straight line connecting the center of the grinding wheel and the center of rotation of the workpiece. The cam profile is obtained through the coordinated machining of the X and C axes, such as... Figure 6 As shown, using the roller tappet model, the relationship between the displacement of the grinding wheel center O2 along the X direction and the rotation angle θ of the roller center O1 is obtained as follows:

[0081] ,

[0082] In the formula, O is the cam center; O1 is the roller center; H(θ) is the relationship between the lift H and the rotation angle θ in the cam lift table; r g r is the roller radius; s r is the radius of the grinding wheel. j Let be the base circle radius of the cam; the relationship between the cam rotation angle α and the rotation angle θ of the roller center O1 is:

[0083] .

[0084] The cam's rectangular coordinates (x, y) are converted to polar coordinates (ρ, φ) from 0 to 2π, as shown in the following formula:

[0085] ;

[0086] The XC axis displacement and rotation table can be obtained from the polar coordinate equation, and the formula is as follows:

[0087] ,

[0088] In the formula, S x C is the distance between the grinding wheel center O2 and the cam center O; C is the cam rotation angle in polar coordinates. ; S x After fitting with C, take the corresponding S at each integer rotation angle of the cam. x And subtract the cam base circle radius r j and grinding wheel radius r s This allows us to obtain the feed displacement of the grinding wheel spindle corresponding to each rotation of the cam workpiece.

[0089] When grinding a camshaft with a grinding wheel, the uneven surface height distribution due to differences in abrasive grain size results in variations in the diameter of the concentric circles formed by the rotating cutting edges around the center of the grinding wheel. Each abrasive grain cuts the camshaft profile along its motion trajectory, generating microscopic marks. These marks, when superimposed on the surface, collectively constitute the final grinding morphology. To accurately characterize this process, a cutting trajectory model of a single abrasive grain needs to be established. Based on the camshaft-grinding wheel constraint relationship described above, the motion trajectory equation of the abrasive grain on the camshaft surface is derived mathematically.

[0090] Based on the formula:

[0091] ,

[0092] In the formula, S x (t) is the real-time distance between the grinding wheel center O2 and the cam center O; then:

[0093] ,

[0094] In the formula, X S (t) and Y S (t) represents the real-time coordinate of the grinding wheel center O2; C(t) represents the real-time polar coordinate rotation angle of the cam, C(t) = ωt, where ω is the angular velocity of the cam; the coordinates of the abrasive grain globally are the superposition of the real-time coordinates of the grinding wheel center O2 and the motion of the abrasive grain in the grinding wheel coordinate system. Let the polar coordinates of the abrasive grain at the grinding wheel center O2 be (r s , θ s (t)), θ s (t)= ω s t, ω s Given the angular velocity of the grinding wheel, the equation for the grinding trajectory of a single abrasive grain can be obtained:

[0095] ,

[0096] In the formula, x g (t) and y g (t) represents the real-time coordinates of the abrasive grain.

[0097] The abrasive grains on the grinding wheel surface are randomly and unevenly distributed, resulting in wheel imbalance during high-speed grinding of non-circular camshaft profiles, causing wheel vibration. The workpiece surface quality is most affected by vibration along the X-direction, leaving vibration marks on the ground surface and significantly impacting grinding quality. Furthermore, high-speed grinding of non-circular camshaft profiles is a plunge grinding process, where the grinding wheel does not move in the Z and Y directions. Therefore, this embodiment primarily considers the vibration of the grinding wheel along the X-direction. By introducing a mathematical model of grinding wheel vibration into the single abrasive grain grinding motion trajectory equation, a single abrasive grain grinding motion trajectory equation considering vibration can be obtained.

[0098] In this embodiment, the mathematical model for the radial vibration of the grinding wheel introduced when establishing the equation for the grinding motion trajectory of a single abrasive grain considering vibration is as follows:

[0099] ,

[0100] In the formula, W k ξ represents the amplitude of the grinding wheel vibration; k This is the initial phase of the grinding wheel vibration signal, which is generally set to 0 in the case of high-speed grinding of non-circular profiles of camshafts; =ω s That is, equal to the angular velocity of the grinding wheel. f is the vibration frequency. ME is the imbalance of the grinding wheel system, and M is the total mass of the grinding wheel system. It is the natural angular frequency of the grinding wheel rotation system, for precision grinding machines. When the amplitude W k Approximately equal to the static deformation W caused by the excitation amplitude k0 At this time, the angular frequency of the grinding wheel is much smaller than the natural frequency of the grinding wheel rotation system. At low frequencies, W k0 Approaching zero, therefore, It is a very small value, let = 1 × 10 -12 m⋅s 2 / rad 2 .

[0101] By incorporating the mathematical model of radial vibration of the grinding wheel into the single-grain grinding motion trajectory equation, the single-grain grinding motion trajectory equation considering vibration is obtained as follows:

[0102] .

[0103] The surface morphology of a workpiece after grinding is the result of the combined action of multiple abrasive grains, with multiple grains participating in the machining process simultaneously. Therefore, the interaction between abrasive grains must be taken into account when constructing the surface morphology. To accurately construct the surface morphology, after establishing the grinding motion trajectory equation of a single abrasive grain considering vibration, it is necessary to further consider the positional relationship and motion state of adjacent abrasive grains. The initial positions of adjacent abrasive grains may differ in the grinding wheel coordinate system, but their motion follows the same rules, and the initial angles of the two abrasive grains are different.

[0104] Let two adjacent abrasive grains be i and j, and the initial angle difference between the two adjacent abrasive grains be... Then we have:

[0105] ;

[0106] ;

[0107] The trajectory difference between two adjacent abrasive grains is:

[0108] ;

[0109] The spacing between two adjacent abrasive grains is:

[0110] .

[0111] By combining the dynamic simulation model of the grinding wheel surface morphology and the grinding motion trajectory equation of a single abrasive grain considering vibration, the grinding surface morphology is generated through the superposition of multiple abrasive grain trajectories, interference and envelope algorithms, and the surface roughness is calculated with the help of the surface morphology data.

[0112] Specifically, step S5 includes: S51. Discretizing the surface of the grinding wheel and the non-circular contour surface of the camshaft; S52. Selecting an axial section of the grinding wheel, extracting its abrasive data, calculating its trajectory and storing it in matrix W(i, j); cyclically iterating through all axial sections until the trajectory of all abrasive grains is covered; S53. When multiple abrasive grain trajectories intersect to form an intersection point, if the height value of the subsequent trajectory at the intersection point is lower, then the lower point is updated as an effective interference point, the lowest point z(m, n) of all trajectories is selected and the matrix W(i, j) is updated to form the workpiece surface contour; S54. Extracting data points that satisfy the surface morphology generation principle from the matrix W(i, j), storing them in matrix Wz(i, j), and generating the grinding surface morphology through an envelope algorithm.

[0113] In summary, the overall logical framework of the dynamic modeling method for surface morphology of non-circular profile high-speed grinding of camshafts provided by this invention is as follows: Figure 7 As shown.

[0114] Simulation Results and Experimental Verification Analysis

[0115] To verify the accuracy of this invention, the detected surface morphology was compared with the simulated surface morphology. The comparison results are as follows: Figure 8 As shown, the detected surface morphology and the simulated surface morphology have the same trend in the Y-direction section. Since the ground surface is a non-circular contour surface with a certain curvature change, the high points are concentrated in the middle, and the trend of change is basically the same as that shown from the curve of the center section in the Y direction.

[0116] After conducting a high-speed grinding experiment on the non-circular profile of the camshaft, the roughness of the ground camshaft was measured. The roughness was measured three times at the tip, lift, base circle, and return stroke, and the average value was taken. The roughness was then compared with the predicted value of the simulation model, as shown in Table 1.

[0117] Table 1 Measured and predicted values ​​of surface roughness

[0118]

[0119] It can be seen that the absolute errors of both the simulation values ​​and the measured values ​​are within 10%, with the minimum absolute error being 2.1% and the maximum absolute error being 9.9%. The absolute errors are approximately consistent with the patterns shown by the roughness measurement values, which verifies the correctness and effectiveness of the proposed model.

[0120] To further verify the model, considering the effect of abrasive wear on the grinding wheel, a full-life test of grinding wheel wear was conducted in the grinding process state data acquisition and grinding process state analysis experiments (v...). s =150 m / s, v w =100 r / min, a p The surface roughness of the first 10 grinding operations (with a roughness of 0.01 mm) was tested, and the roughness value was predicted using the proposed simulation model. Similarly, six measurements were taken at each location, and the average value was recorded, as shown in Table 2.

[0121] Table 2. Measured and predicted values ​​of grinding surface roughness considering grinding wheel wear.

[0122]

[0123] For ease of comparison, the measured and predicted surface roughness values ​​of the base circle portion are selected, such as... Figure 9 As shown. From Figure 9It can be seen that the overall error between the measured and predicted values ​​is controlled within 13%, with two instances of larger errors, approximately 12.2%. This is due to the internal stress and cracks present in the newly dressed grinding wheel, causing a temporary increase in surface roughness. The dressing process introduces internal stress and micro-cracks into the abrasive grains, making them prone to breakage and detachment during grinding. This results in rapid abrasive wear and an increasing contact area between the abrasive grains and the cam, leading to increased tangential grinding force. Consequently, a temporary increase in surface roughness occurs during actual grinding. However, as grinding progresses, the grinding wheel enters the normal wear stage. At this point, the abrasive grains have sharp cutting edges, efficiently removing material through shearing. Consequently, the tangential grinding force gradually decreases, leading to a reduction in surface roughness. Analysis shows that as grinding progresses, the surface roughness value initially decreases and then increases with increasing wear. However, since this section only discusses the first ten tests, focusing primarily on the initial and stable wear stages of the grinding wheel, it can be observed that both the tested and simulated roughness values ​​initially increase and then decrease, eventually fluctuating steadily at a relatively low level. If the simulation model fails to consider the wear of the grinding wheel abrasive grains, the predicted roughness value will fluctuate within a certain range without changing with the accumulation of grinding wheel wear. Furthermore, as grinding progresses, the surface roughness value that does not consider grinding wheel wear will deviate more and more from the actual surface roughness value until it completely deviates from the actual value. From the trends and errors of the simulated and predicted roughness values, it can be seen that the grinding surface morphology model that considers grinding wheel wear and vibration is closer to the actual ground surface.

[0124] In summary, this dynamic modeling method for the surface morphology of non-circular profile high-speed grinding of camshafts can effectively simulate the continuous wear of the grinding wheel and the influence of vibration on the surface morphology during the grinding process. It achieves dynamic modeling of the surface morphology, with high simulation accuracy, and can provide more accurate guidance for the optimization of machining process parameters.

[0125] Where there is no conflict, the above embodiments and features can be combined with each other.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the preferred technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the present invention.

Claims

1. A method for dynamic modeling of the surface morphology of a camshaft with a non-circular profile during high-speed grinding, characterized in that, Includes the following steps: S1. Acquire mixed signals during the high-speed grinding process of the non-circular profile of the camshaft using acoustic emission sensors and vibration sensors. Preprocess the mixed signals and perform blind source separation to obtain the source signal components corresponding to the wear of the grinding wheel. S2. Extract time-domain and frequency-domain signal features from the source signal components, select signal features that are highly correlated with grinding wheel wear, and combine them with the grinding wheel abrasive wear area to construct an online abrasive wear prediction model based on FAW-DELM. Predict the real-time grinding wheel abrasive wear area through real-time source signal components. FAW-DELM is a parameter optimization model for the input layer weights and offset thresholds of the deep extreme learning machine using the fireworks algorithm. S3. Measure the surface morphology of the grinding wheel, using a triangular pyramid to simulate the abrasive grain shape. Set the abrasive grain protrusion height to follow a normal distribution, where the mean of the normal distribution represents the abrasive grain protrusion height, and the variance represents the abrasive grain distribution. As the grinding wheel wears, the protrusion height decreases but the distribution remains constant. Calculate the abrasive grain protrusion height using the real-time abrasive grain wear area obtained in step S2, dynamically adjust the mean of the normal distribution, and obtain a dynamic normal distribution model for the abrasive grain protrusion height. Combine this with the spatial distribution calculation results of the abrasive grains obtained during the measurement of the grinding wheel surface morphology to establish a dynamic simulation model of the grinding wheel surface morphology. The dynamic normal distribution model for the abrasive grain protrusion height is as follows: ， In the formula, H g The abrasive grain exit height is represented by σ; σ represents the variance of the normal distribution, σ = (D max -D min ) / 8;D max D represents the maximum height of the abrasive grain exiting the cutting edge. min The minimum abrasive grain protrusion height is represented by the values ​​measured during the morphology measurement of the grinding wheel surface; ψ represents the apex angle of the triangular pyramid; S w (t) represents the wear area of ​​the grinding wheel abrasive grains at the previous moment; S4. Based on the grinding parameters and the motion relationship of the XC axis linkage grinding of the camshaft, establish the motion trajectory equation of single abrasive grinding; simplify the radial vibration of the grinding wheel along the X direction into simple harmonic motion, introduce radial vibration into the motion trajectory equation of single abrasive grinding, and obtain the motion trajectory equation of single abrasive grinding considering vibration. S5. Combining the dynamic simulation model of the grinding wheel surface morphology and the single abrasive grinding motion trajectory equation considering vibration, the grinding surface morphology is generated through the superposition of multiple abrasive trajectories, interference and envelope algorithms, and the surface roughness is calculated with the help of the surface morphology data.

2. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, In step S1, the preprocessing includes outlier detection and optimization procedures: First, the original signal is divided into multiple signal segments; Then, the signal segment is further divided into several signal parts. If the root mean square value of a certain signal part exceeds the set threshold, the signal part is regarded as an outlier. The threshold is derived according to the 3σ principle. Finally, outliers are removed from the original signal and the data is supplemented by linear interpolation.

3. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, In step S1, blind source separation employs a signal processing method based on WPD-EWT-FastICA, which includes: The acoustic emission signal was processed using the WPD-FastICA method with a sampling frequency of 1MHz. Wavelet packet decomposition was used for three-level decomposition, and the db10 wavelet was selected as the wavelet basis function. The frequency band node signal with the highest energy proportion was selected from the decomposed node signal to construct the input matrix, and the independent components were separated by the FastICA algorithm. The vibration signal was processed using the EWT-FastICA method with a sampling frequency of 6400Hz. Empirical wavelet transform was used for decomposition, and the Fourier spectrum of the signal was adaptively segmented. The frequency band boundary was determined based on the spectral maxima. An empirical wavelet filter bank was constructed, and the decomposed components were used to construct an input matrix. The independent components were then separated using the FastICA algorithm.

4. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, In step S2, the signal features that are highly correlated with grinding wheel wear include the root mean square value of the acoustic emission signal, the centroid frequency of the acoustic emission signal, the root mean square value of the vibration signal, the variance of the vibration signal, the skewness of the vibration signal, and the centroid frequency of the vibration signal.

5. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, In step S2, the population size of the fireworks algorithm is set to 100, and the maximum number of iterations is 100; the deep limit learning machine is a 3-layer deep structure with 60 input neurons in each layer and the activation function of the hidden layer is Sigmoid.

6. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, In step S4, the method for establishing the motion trajectory equation of a single abrasive grain grinding is as follows: Using the roller tappet model, the relationship between the displacement of the grinding wheel center O2 along the X direction and the rotation angle θ of the roller center O1 is obtained as follows: ， In the formula, O is the cam center; O1 is the roller center; H(θ) is the relationship between the lift H and the rotation angle θ in the cam lift table; r g r is the roller radius; s r is the radius of the grinding wheel. j The base circle radius of the cam; The relationship between the cam rotation angle α and the rotation angle θ of the roller center O1 is: ； The cam's rectangular coordinates (x, y) are converted to polar coordinates (ρ, φ) from 0 to 2π, as shown in the following formula: ； The XC axis displacement and rotation table can be obtained from the polar coordinate equation, and the formula is as follows: ， In the formula, S x C is the distance between the grinding wheel center O2 and the cam center O; C is the cam rotation angle in polar coordinates. ; ; Based on the formula: ， In the formula, S x (t) represents the real-time distance between the grinding wheel center O2 and the cam center O; Then we have: ， In the formula, X S (t) and Y S C(t) is the real-time coordinate of the grinding wheel center O2; C(t) is the real-time polar coordinate rotation angle of the cam, C(t) = ωt, where ω is the angular velocity of the cam; The global coordinates of the abrasive grain are the superposition of the real-time coordinates of the grinding wheel center O2 and the motion of the abrasive grain in the grinding wheel coordinate system. Let the polar coordinates of the abrasive grain at the grinding wheel center O2 be (r s , θ s (t)), θ s (t)= ω s t, ω s Given the angular velocity of the grinding wheel, the equation for the grinding trajectory of a single abrasive grain can be obtained: ， In the formula, x g (t) and y g (t) represents the real-time coordinates of the abrasive grain.

7. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 6, characterized in that, In step S4, the mathematical model for the radial vibration of the grinding wheel introduced when establishing the equation of motion trajectory of a single abrasive grain considering vibration is as follows: ， In the formula, W k ξ represents the amplitude of the grinding wheel vibration; k The initial phase of the grinding wheel vibration signal is set to 0. =ω s ; ,set up = 1 × 10 -12 m⋅s 2 / rad 2 ; By incorporating the mathematical model of radial vibration of the grinding wheel into the single-grain grinding motion trajectory equation, the single-grain grinding motion trajectory equation considering vibration is obtained as follows: ； Let two adjacent abrasive grains be i and j, and the initial angle difference between the two adjacent abrasive grains be... Then we have: ； ； The trajectory difference between two adjacent abrasive grains is: ； The spacing between two adjacent abrasive grains is: 。 8. The method for dynamic modeling of surface morphology in high-speed grinding of non-circular profiles of camshafts according to claim 1, characterized in that, Step S5 includes: S51. Discretize the grinding wheel surface and the non-circular profile surface of the camshaft; S52. Select an axial section of the grinding wheel, extract its abrasive grain data, calculate its trajectory and store it in matrix W(i, j); iterate through all axial sections in turn until the trajectory of all abrasive grains is covered; S53. When multiple abrasive grain trajectories intersect to form an intersection point, if the height value of the subsequent trajectory at the intersection point is lower, then update the lower point as an effective interference point, filter the lowest point z(m, n) of all trajectories and update the matrix W(i, j) to form the workpiece surface contour; S54. Extract data points that satisfy the surface morphology generation principle from matrix W(i, j), store them in matrix Wz(i, j), and generate the grinding surface morphology through the envelope algorithm.

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