Method for calculating elastic-plastic-brittleness critical grinding force of titanium-aluminum alloy based on wavelet transformation model

Abstract

The invention relates to a method for calculating elastic-plastic-brittle critical grinding force of a titanium-aluminum alloy based on a wavelet transformation model, which comprises the following steps of: acquiring a grinding force signal, establishing a tangential grinding force data sample, determining a scale function and a wavelet function, and decomposing grinding force data to obtain a low-frequency signal and a high-frequency signal. High-frequency data are extracted, and low-frequency data are subjected to signal reconstruction; and titanium-aluminum alloy grinding elastic-plastic-brittle transition critical conditions are identified. According to the method, original tangential grinding force signals are decomposed through wavelet transformation, critical points of elastic, plastic and brittle transformation of the titanium-aluminum alloy and critical normal grinding force and tangential grinding force corresponding to the critical points can be accurately recognized, and high-precision recognition of the critical transformation points, efficient signal separation and reconstruction and adaptation to non-stationary signal processing are achieved; the problem that elastic, plastic and brittle transition critical points are difficult to identify in the existing titanium-aluminum alloy grinding machining process is solved, plastic domain machining of materials is achieved, and the machining quality of workpieces is improved.

Description

Technical Field

[0001] The invention belongs to the field of titanium-aluminium alloy grinding, and in particular relates to a method for calculating a critical grinding force of a ductile-brittle transition of a titanium-aluminium alloy. Background Art

[0002] The adhesion of the grinding wheel is serious during grinding. Due to the particularity of the process, it is difficult for the coolant to enter the grinding arc area, resulting in high grinding force and grinding temperature during the grinding process. The intrinsic brittleness of titanium aluminum alloy makes it a typical difficult-to-process material. The coupling effect of grinding force and grinding heat will cause it to easily produce residual tensile stress, microscopic and potential cracks during the grinding process, greatly reducing its surface state, becoming a potential fatigue source for components, and significantly affecting the fatigue life and service reliability of components. When the grinding force of the abrasive is lower than a certain critical value, the titanium aluminum alloy material will be in the plastic domain removal mode, and the plastic domain removal mode is conducive to reducing processing damage. Therefore, accurate calculation of the critical grinding force of the plastic-brittle transition of titanium aluminum alloy grinding is helpful to improve the processing quality of the workpiece.

[0003] In addition, the plastic-brittle transition itself has the characteristics of suddenness, and the transition process is fast and not obvious, which further increases the difficulty of accurate identification. Therefore, when directly observing the surface morphology and analyzing the original scratch force signal, it becomes particularly difficult to accurately identify the critical point of the elastic-plastic-brittle transition and obtain the normal grinding force and tangential grinding force corresponding to the critical point. Summary of the invention

[0004] The purpose of the present invention is to avoid the shortcomings of the prior art and provide a method for identifying the critical points of the elastic-plastic-brittle transition of titanium-aluminum alloys through wavelet transformation, and accurately obtain the critical normal grinding force and tangential grinding force corresponding to the critical point, a method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloys based on a wavelet transformation model.

[0005] To achieve the above object, the technical solution adopted by the present invention is a method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on a wavelet transform model, comprising the following steps: Step 1: collecting the grinding force signal during the variable cutting depth grinding process of titanium aluminum alloy, extracting the tangential grinding force signal in the grinding force signal, and establishing the original tangential grinding force data sample; Step 2: Selecting a Db wavelet basis function of any order of the tangential grinding force through the original tangential grinding force data sample, thereby obtaining a scaling function and a wavelet function corresponding to the Db wavelet basis function; Step 3, projecting the original tangential grinding force data samples onto the scaling function and the wavelet function, that is, decomposing the original tangential grinding force data samples into low-frequency signals and high-frequency signals of the tangential grinding force; Step 4: high-pass filter the low-frequency signal and the high-frequency signal of the tangential grinding force to obtain high-frequency data corresponding to the high-frequency signal of the tangential grinding force, and establish a high-frequency data sample; and use the low-frequency data corresponding to the low-frequency signal remaining after high-pass filtering to establish a low-frequency data sample; Step 5: Based on the inverse transform process of wavelet transform, reconstruct the low-frequency signal remaining after high-pass filtering, obtain the low-frequency reconstructed signal and the low-frequency reconstructed data corresponding to the low-frequency reconstructed signal, and establish the low-frequency reconstructed data sample; Step 6, measuring the tangential grinding force fluctuation frequency values ​​of the original tangential grinding force data sample and the low-frequency reconstructed data sample, and repeating steps 2 to 6 to compare the tangential grinding force fluctuation frequency values. When the tangential grinding force fluctuation frequency value changes from a fluctuating change to a smooth and continuous one, and the low-frequency reconstructed signal data value of the low-frequency reconstructed data sample remains within the range of the original tangential grinding force data sample, the order determined by the Db wavelet basis function is obtained; Step seven, using the Db wavelet basis function corresponding to the order, repeat steps three to four, continuously update the low-frequency and high-frequency data samples of the tangential grinding force, and project the updated low-frequency data samples onto the scale function and wavelet function of the Db wavelet basis function corresponding to the order, until the high-frequency data samples established by decomposing the updated tangential grinding force high-frequency signal can obtain the critical time point showing the elastic, plastic and brittle transition characteristics of the titanium aluminum alloy material on the timeline of the grinding process. The grinding force corresponding to the critical time point is the critical grinding force of the elastic, plastic and brittle transition.

[0006] Furthermore, the grinding force signal described in step 1 is selected from the grinding force signal data obtained by a desktop dynamometer during the period from 1 second after the grinding wheel enters the cutting blade to 1 second before the grinding wheel retracts the cutting blade, so as to ensure the stability of the data; In step one, a signal image of the tangential grinding force is extracted from the overall grinding process monitoring data, the grinding time and the grinding force frequency are extracted from the signal image, and then the grinding time, the grinding force frequency and the tangential grinding force values ​​corresponding to the grinding time and the grinding force frequency are used as the original tangential grinding force data samples.

[0007] Furthermore, the Db wavelet basis function described in step 2 is: , In the formula, represents the Db wavelet basis mother function, is the discrete dyadic wavelet basis function, represents the scale factor, n represents the displacement factor; Then, the scaling function corresponding to the Db wavelet basis function is: , In the formula, represents the scaling function, h m,n represents the filter coefficients of the scaling function, i.e. the low-pass filter coefficients, N is the order of Db wavelet basis function; The wavelet function corresponding to the Db wavelet basis function is: , In the formula, represents the wavelet function, g m,n represents the filter coefficients of the wavelet function, that is, the high-pass filter coefficients, N is the order of Db wavelet basis function; Among them, the high-pass filter coefficient g m,n pass Calculated.

[0008] Furthermore, the projection process of the original tangential grinding force data sample onto the scale function and the wavelet function in step 3 is represented by the inner product operation between the original tangential grinding force data sample and the wavelet basis function as follows: , In the formula, DWT F ( m , n ) represents the discrete wavelet transform signal processing process, <> and represent inner product operation and conjugate complex number respectively, F ( t ) represents the tangential grinding force data sample, is the discrete dyadic wavelet basis function, m represents the scale factor, n represents the displacement factor; Next, the projected data are projected onto the scaling function and the wavelet function. Specifically, the original tangential grinding force data samples are decomposed into low-frequency signals and high-frequency signals. The expressions of the low-frequency signals and the high-frequency signals are: , , In the formula, <> and represent inner product operation and conjugate complex number respectively, F ( t ) represents the original tangential grinding force signal, represents the decomposed low-frequency signal, represents the decomposed high-frequency signal, h m,n represents the low-pass filter coefficient, g m,n Represents the high-pass filter coefficients.

[0009] Furthermore, the expression of the inverse transformation process of the wavelet transform in step 5 is: ， In the formula represents the low-frequency reconstructed signal, J represents the number of decompositions, h m,n Indicates m Second decomposition, n The low-pass filter coefficients.

[0010] Furthermore, on the timeline of the grinding process, there are: The first stage: the amplitude of the high-frequency data sample is relatively small and remains stable, indicating that the material is in the elastic deformation stage; The second stage: the amplitude of the high-frequency data sample increases relatively, and as the deformation continues, it shows an overall upward trend, which indicates that the material has entered the elastic-plastic deformation stage; The third stage: The amplitude of the high-frequency data sample suddenly increases sharply, indicating that the material has entered the stage of transition from plasticity to brittleness; The relative increase time point of the amplitude of the high-frequency data samples in the second stage is taken as the critical time point of the elastic-plastic transformation characteristics of the titanium-aluminum alloy material. The tangential grinding force and normal grinding force corresponding to the critical time point are the critical grinding forces of the elastic-plastic transformation. The time point of the sudden increase in the amplitude of the high-frequency data samples in the third stage is taken as the critical time point of the ductile-brittle transition characteristics of the titanium-aluminum alloy material, and the corresponding tangential grinding force and normal grinding force are the critical grinding forces of the ductile-brittle transition.

[0011] Furthermore, the fourth stage is when the amplitude of the high-frequency data sample no longer follows any obvious rules, indicating that the material has completely transformed into the brittle fracture removal stage. At this time, the grinding force corresponding to the time point when the amplitude no longer follows any obvious rules is the critical grinding force of complete brittle transformation.

[0012] The beneficial effects of the present invention are as follows: the method provided by the present invention can accurately calculate the critical grinding force of the plastic-brittle transition of titanium aluminum alloy during the grinding process, realize the plastic domain processing of the material, and improve the processing quality of the workpiece, which specifically includes the following advantages: (1) High-precision identification of critical transition points: The method of the present invention uses wavelet transform to decompose the original tangential grinding force signal, which can accurately identify the critical normal grinding force and the corresponding critical tangential grinding force of the titanium aluminum alloy from plasticity to brittleness. This overcomes the difficulty in accurately identifying the critical point of plastic-brittle transition when directly observing the surface morphology and analyzing the original signal, resulting in the inability to obtain the critical grinding force; (2) Efficient signal separation and reconstruction: Through wavelet transform, the low-frequency signal and high-frequency signal in the original tangential grinding force signal can be effectively separated; at the same time, the inverse transform of wavelet transform can be used to accurately reconstruct the low-frequency signal to ensure that the basic characteristics of the signal are preserved, providing a reliable data basis for subsequent material performance analysis; (3) Adaptation to non-stationary signal processing: This method adopts a flexible wavelet basis function selection and adjusts and optimizes it according to specific needs. By introducing scale factors and displacement factors, it can flexibly analyze the local characteristics of the signal, which has significant advantages in processing non-stationary signals generated during the grinding process of titanium-aluminum alloy. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the present invention; Figure 2 It is a schematic diagram of tangential grinding force data of the present invention; Figure 3 It is a schematic diagram of decomposing the tangential grinding force signal three times according to the present invention; Figure 4 It is a schematic diagram of the high-frequency signal of the tangential grinding force extracted by the present invention; Figure 5 It is a schematic diagram of the reconstruction signal of the low-frequency signal of the tangential grinding force of the present invention; Figure 6 Schematic diagram of identifying the critical conditions of ductile-brittle transition in the present invention. DETAILED DESCRIPTION

[0014] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0015] In order to achieve the above object, the present invention provides the following specific embodiments: Embodiment 1: A method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on a wavelet transform model, comprising the following steps: S01. Grinding force signals are collected during the variable cutting depth grinding process of titanium aluminum alloy. The grinding force signal data obtained by the desktop dynamometer during the period from 1 second after the grinding wheel enters the cutting wheel to 1 second before the grinding wheel retracts the cutting wheel is selected to ensure the stability of the data.

[0016] S02. Extract the signal image of the tangential grinding force from the overall grinding process monitoring data, extract the grinding time and the grinding force frequency from the signal image, and then use the grinding time, the grinding force frequency and the tangential grinding force values ​​corresponding to the grinding time and the grinding force frequency as original tangential grinding force data samples, and establish the original tangential grinding force data samples.

[0017] S03. The Db wavelet basis function of any order of tangential grinding force is selected through the original tangential grinding force data sample: , In the formula, represents the Db wavelet basis mother function, is the discrete dyadic wavelet basis function, represents the scale factor, n Represents the displacement factor.

[0018] S04. The scaling function corresponding to the obtained Db wavelet basis function is: , In the formula, represents the scaling function, h m,n represents the filter coefficients of the scaling function, i.e. the low-pass filter coefficients, N is the order of the Db wavelet basis function.

[0019] S05. The wavelet function corresponding to the obtained Db wavelet basis function is: , In the formula, represents the wavelet function, g m,n represents the filter coefficients of the wavelet function, that is, the high-pass filter coefficients, N is the order of Db wavelet basis function; Among them, the high-pass filter coefficient g m,n pass Calculated.

[0020] S06. The process of projecting the original tangential grinding force data sample onto the scale function and the wavelet function is represented by the inner product operation between the original tangential grinding force data sample and the wavelet basis function: , In the formula, DWT F (m,n) represents the discrete wavelet transform signal processing process, and <> and represent inner product operation and conjugate complex number respectively, F ( t ) represents the tangential grinding force data sample, is the discrete dyadic wavelet basis function, m represents the scale factor, n represents the displacement factor; Next, the projected data are projected onto the scaling function and the wavelet function. Specifically, the original tangential grinding force data samples are decomposed into low-frequency signals and high-frequency signals. The expressions of the low-frequency signals and the high-frequency signals are: , , In the formula, <> and represent inner product operation and conjugate complex number respectively, F ( t ) represents the original tangential grinding force signal, represents the decomposed low-frequency signal, represents the decomposed high-frequency signal, h m,n represents the low-pass filter coefficient, g m,n Represents the high-pass filter coefficients.

[0021] S07, high-pass filtering is performed on the low-frequency signal and the high-frequency signal of the tangential grinding force to obtain high-frequency data corresponding to the high-frequency signal of the tangential grinding force, and a high-frequency data sample is established; and the low-frequency data corresponding to the low-frequency signal remaining after the high-pass filtering is used to establish a low-frequency data sample.

[0022] S08. Expression of the inverse transformation process based on wavelet transform: ， In the formula represents the low-frequency reconstructed signal, J represents the number of decompositions, h m,n Indicates m Second decomposition, n low-pass filter coefficients; reconstruct the low-frequency signal remaining after the high-pass filtering, obtain the low-frequency reconstructed signal and the low-frequency reconstructed data corresponding to the low-frequency reconstructed signal, and establish the low-frequency reconstructed data sample.

[0023] S09, measuring the tangential grinding force fluctuation frequency values ​​of the original tangential grinding force data samples and the low-frequency reconstructed data samples.

[0024] S10, repeat S03 to S09 to compare the tangential grinding force fluctuation frequency values. When the tangential grinding force fluctuation frequency value changes from fluctuation to smooth continuity, and the low-frequency reconstructed signal data value of the low-frequency reconstructed data sample remains within the range of the original tangential grinding force data sample, the order determined by the Db wavelet basis function is obtained. N .

[0025] S11, Use order N The corresponding Db wavelet basis function is repeated from S06 to S07 to continuously update the low-frequency and high-frequency data samples of the tangential grinding force. N The corresponding scaling function of the Db wavelet basis function is projected onto the wavelet function.

[0026] S12, until the high-frequency data samples established by decomposing the updated tangential grinding force high-frequency signal are sequentially: The first stage: the amplitude of the high-frequency data sample is relatively small and remains stable, indicating that the material is in the elastic deformation stage; The second stage: the amplitude of the high-frequency data sample increases relatively, and as the deformation continues, it shows an overall upward trend, which indicates that the material has entered the elastic-plastic deformation stage; The third stage: The amplitude of the high-frequency data sample suddenly increases sharply, indicating that the material has entered the stage of transition from plasticity to brittleness; The fourth stage: When the amplitude of the high-frequency data sample no longer follows any obvious rules, it indicates that the material has completely transformed into the brittle fracture removal stage. At this time, the grinding force corresponding to the time point when the amplitude no longer follows any obvious rules is the critical grinding force of complete brittle transformation; The relative increase time point of the amplitude of the high-frequency data samples in the second stage is taken as the critical time point of the elastic-plastic transformation characteristics of the titanium-aluminum alloy material. The tangential grinding force and normal grinding force corresponding to the critical time point are the critical grinding forces of the elastic-plastic transformation. The time point of the sudden increase in the amplitude of the high-frequency data samples in the third stage is taken as the critical time point of the ductile-brittle transition characteristics of the titanium-aluminum alloy material, and the corresponding tangential grinding force and normal grinding force are the critical grinding forces of the ductile-brittle transition.

[0027] like Figures 1 to 6 As shown, in order to further illustrate the technical solution and technical effects of the present invention, the present invention provides the following specific experimental examples. It should be noted that the full name of the Db wavelet basis function described in the present invention is Daubechies wavelet basis function. When written as DbN, N is the order of the corresponding wavelet basis function.

[0028] Specific experimental example: Figure 1 As shown in the figure, a diamond abrasive with a diameter of 40 μm and a blade height of 80 μm is used to grind a titanium aluminum alloy workpiece with a size of 20×20×10 mm by single abrasive grinding. The grinding speed is 500 mm / min, the variable cutting depth is 0-13 μm, and the grinding time is 8 s. The titanium aluminum alloy variable cutting depth grinding process is carried out under the conditions. The specific calculation steps of the critical grinding force of the ductile-brittle transition based on the wavelet transform model are as follows: Step 1: Collect the grinding force signal during the variable cutting depth grinding process of titanium aluminum alloy, extract the tangential grinding force signal, and establish the data sample required for the decomposition of the original tangential grinding force, such as Figure 2 shown.

[0029] Step 2: The wavelet basis function selected in the experimental example is the Db5 wavelet basis function. The tangential force data samples are discrete points, so the discrete binary Db5 wavelet function used is: , In the formula, represents the Db wavelet basis mother function, is the discrete dyadic wavelet basis function, represents the scale factor, n represents the displacement factor; The corresponding scaling function and wavelet function are: , , In the formula, represents the scaling function, h m,n represents the filter coefficients of the scaling function, i.e. the low-pass filter coefficients, N is the order of Db wavelet basis function; represents the wavelet function, g m,n represents the filter coefficients of the wavelet function, that is, the high-pass filter coefficients, N is the order of Db wavelet basis function; The tangential grinding force data samples are imported into the MATLAB software through the Load Data command, and a wavelet analysis program is written. The Db5 wavelet basis function is selected to be used. The program will calculate the scale factor and displacement factor based on the Db5 wavelet basis function and the tangential grinding force data samples.

[0030] Step 3, Experimental Example The original tangential grinding force data samples are projected onto the scaling function and the wavelet function, that is, the original tangential grinding force data samples are decomposed into the low-frequency signal and the high-frequency signal of the tangential grinding force. The specific expression is: , , , In the formula, <> and represent inner product operation and conjugate complex number respectively, F ( t ) represents the original tangential grinding force signal, represents the decomposed low-frequency signal, represents the decomposed high-frequency signal, h m,n represents the low-pass filter coefficient, g m,n Represents the high-pass filter coefficients.

[0031] Step 4: Obtain high-frequency data corresponding to the high-frequency signal of the tangential grinding force and establish a high-frequency data sample, such as Figure 4 As shown; and using the remaining low-frequency signal after high-pass filtering, the low-frequency data sample is established.

[0032] Step 5: Based on the inverse transform process of wavelet transform, the low-frequency signal remaining after high-pass filtering is reconstructed to obtain the low-frequency reconstructed signal and the low-frequency reconstructed data corresponding to the low-frequency reconstructed signal, and establish the low-frequency reconstructed data sample; the specific expression is: ， In the formula Reconstruct the signal for low frequencies, J represents the number of decompositions, h m,n Indicates the decomposition m sequence n The low-pass filter coefficients.

[0033] Step 6. Measure the tangential grinding force fluctuation frequency and numerical value of the original tangential grinding force data samples and the low-frequency reconstructed data samples. It can be seen that the reconstructed signal fluctuation frequency is transformed from a fluctuating line to a smooth curve, and the numerical value remains within the range of the original tangential grinding force data samples, proving that the selected Db5 wavelet basis function is significant. The processing process of the original tangential grinding force data can successfully separate its high-frequency signal, so the order determined by the Db wavelet basis function is 5.

[0034] Step 7, using the Db wavelet basis function corresponding to order 5, repeat steps 3 to 4, continuously update the low-frequency and high-frequency data samples, and project the updated low-frequency data samples onto the scale function and wavelet function of the Db wavelet basis function corresponding to order 5. After the experiment is repeated three times, the normal grinding force or tangential grinding force values ​​of the elastic, plastic and brittle critical points of the titanium aluminum alloy material corresponding to the grinding tangential force are obtained. After calculation, it can be obtained that the critical time point of elastic-plastic transition is 2.10s, and the critical normal grinding force and tangential grinding force are 7.13N and 2.02N respectively; the critical time point of plastic-brittle transition is 3.11s, and the critical normal grinding force and tangential grinding force are 11.51N and 4.13N respectively; the critical time point of complete brittleness is 4.12s, and the critical normal grinding force and tangential grinding force are 15.84N and 6.44N respectively.

[0035] like Figure 3As shown, the wavelet basis function selected in the specific implementation is Db5, and the scaling function and wavelet function corresponding to the wavelet basis function Db5 obtained in step 1 are projected onto the original tangential grinding force data sample into a low-frequency signal CA and a high-frequency signal CD. In this specific example, after repeating steps 3-7 three times, the characteristic performance of the critical condition of the ductile-brittle transition of titanium-aluminum alloy grinding becomes clearly discernible. Among them, the original signal is the original tangential grinding force data, CA1 and CD1 are the low-frequency signal and high-frequency signal of the first decomposition, CA2 and CD2 are the low-frequency signal and high-frequency signal of the second decomposition, and CA3 and CD3 are the low-frequency signal and high-frequency signal of the third decomposition.

[0036] like Figure 5 As shown, in the specific implementation, according to step 5, the low-frequency signal after the third decomposition is reconstructed, and the comparative analysis results between the original tangential grinding force data and the reconstructed signal are shown in Figure 5 As shown, (a), (b), (c), and (d) are local enlarged views of the two. According to step 6, the evaluation results are as follows: the frequency component of the reconstructed signal is significantly reduced, and the numerical value is highly consistent with the original tangential grinding force data, proving that the selected Db5 wavelet basis function is significant, indicating that the processing of the original tangential grinding force data can successfully separate its high-frequency signal and retain the basic characteristics of the original tangential grinding force signal.

[0037] like Figure 6 As shown, in the specific implementation, according to step 7, the critical condition characteristics of the plastic-brittle transition of the third high-frequency data sample of titanium-aluminum alloy grinding that was successfully extracted were evaluated. The results show that when the grinding time is less than 2.10s, the high-frequency signal fluctuates slowly as a whole, and the material is in the elastic deformation stage at this time; when the grinding time is between 2.10s and 3.11s, the high-frequency signal has a small mutation, which makes the signal amplitude increase at the elastic-plastic transition, and as the plastic deformation continues, the signal amplitude increases as a whole, which indicates that the material enters the elastic-plastic deformation stage; when the grinding time is between 3.11s and 4.12s, the signal amplitude suddenly increases sharply, mainly because the deformation mode of the material begins to change from plastic deformation to brittle fracture, and at the same time, a high stress concentration is generated near the diamond indenter. At this time, the grinding force corresponding to the grinding time of 3.11s is the critical grinding force of the plastic-brittle transition, and this stage is the plastic-brittle transition stage; when the grinding time exceeds 4.12s, the signal amplitude begins to no longer follow any obvious rules, which indicates that the material has completely changed to the brittle fracture removal stage.

[0038] In the traditional method of directly observing the surface morphology and analyzing the original signal to identify the critical points of elastic, brittle and plastic transitions, the complexity of the surface morphology makes it difficult to accurately judge the elastic, brittle and plastic transitions of the material with the naked eye or simple instruments; and traditional signal processing methods, such as Fourier transform, are not effective when processing non-stationary and non-periodic signals, and it is difficult to accurately capture their time-frequency characteristics, thus affecting the accurate identification of brittle-plastic transitions. However, by adopting the method of the present invention, the critical point of plastic-brittle transition of titanium aluminum alloy can be accurately identified through the frequency decomposition of the tangential grinding force signal, and the corresponding critical grinding force can be calculated. Through monitoring and measurement during the actual processing process, the workpiece is processed using the plastic domain determined by the present invention, which not only ensures low damage to the material surface and surface layer, optimizes the surface quality, protects the surface structure, but also improves processing efficiency and reduces costs.

[0039] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on wavelet transform model, characterized in that: The following steps are involved: Step 1: collecting the grinding force signal during the variable cutting depth grinding process of titanium aluminum alloy, extracting the tangential grinding force signal in the grinding force signal, and establishing the original tangential grinding force data sample; Step 2: Selecting a Db wavelet basis function of any order of the tangential grinding force through the original tangential grinding force data sample, thereby obtaining a scaling function and a wavelet function corresponding to the Db wavelet basis function; Step 3, projecting the original tangential grinding force data samples onto the scaling function and the wavelet function, that is, decomposing the original tangential grinding force data samples into low-frequency signals and high-frequency signals of the tangential grinding force; Step 4: high-pass filter the low-frequency signal and the high-frequency signal of the tangential grinding force to obtain high-frequency data corresponding to the high-frequency signal of the tangential grinding force, and establish a high-frequency data sample; and use the low-frequency data corresponding to the low-frequency signal remaining after high-pass filtering to establish a low-frequency data sample; Step 5: Based on the inverse transform process of wavelet transform, reconstruct the low-frequency signal remaining after high-pass filtering, obtain the low-frequency reconstructed signal and the low-frequency reconstructed data corresponding to the low-frequency reconstructed signal, and establish the low-frequency reconstructed data sample; Step 6, measuring the tangential grinding force fluctuation frequency values ​​of the original tangential grinding force data sample and the low-frequency reconstructed data sample, and repeating steps 2 to 6 to compare the tangential grinding force fluctuation frequency values. When the tangential grinding force fluctuation frequency value changes from a fluctuating change to a smooth and continuous one, and the low-frequency reconstructed signal data value of the low-frequency reconstructed data sample remains within the range of the original tangential grinding force data sample, the order determined by the Db wavelet basis function is obtained; Step seven, using the Db wavelet basis function corresponding to the order, repeat steps three to four, continuously update the low-frequency and high-frequency data samples of the tangential grinding force, and project the updated low-frequency data samples onto the scale function and wavelet function of the Db wavelet basis function corresponding to the order, until the high-frequency data samples established by decomposing the updated tangential grinding force high-frequency signal can obtain the critical time point showing the elastic, plastic and brittle transition characteristics of the titanium aluminum alloy material on the timeline of the grinding process. The grinding force corresponding to the critical time point is the critical grinding force of the elastic, plastic and brittle transition.

2. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on the wavelet transform model according to claim 1 is characterized in that: The grinding force signal described in step 1 is the grinding force signal data obtained by a desktop dynamometer during the period from 1 second after the grinding wheel enters the cutting blade to 1 second before the grinding wheel retracts the cutting blade, so as to ensure the stability of the data; In step one, a signal image of the tangential grinding force is extracted from the overall grinding process monitoring data, the grinding time and the grinding force frequency are extracted from the signal image, and then the grinding time, the grinding force frequency and the tangential grinding force values ​​corresponding to the grinding time and the grinding force frequency are used as the original tangential grinding force data samples.

3. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on wavelet transform model as claimed in claim 1, characterized in that: The Db wavelet basis function described in step 2 is: ， In the formula, represents the Db wavelet basis mother function, is the discrete dyadic wavelet basis function, represents the scale factor, n represents the displacement factor; Then, the scaling function corresponding to the Db wavelet basis function is: ， In the formula, represents the scaling function, h m,n represents the filter coefficients of the scaling function, i.e. the low-pass filter coefficients, N is the order of Db wavelet basis function; The wavelet function corresponding to the Db wavelet basis function is: ， In the formula, represents the wavelet function, g m,n represents the filter coefficients of the wavelet function, that is, the high-pass filter coefficients, N is the order of Db wavelet basis function; Among them, the high-pass filter coefficient g m,n pass Calculated.

4. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on wavelet transform model as claimed in claim 1, characterized in that: The projection process of the original tangential grinding force data sample onto the scale function and the wavelet function in step 3 is represented by the inner product operation between the original tangential grinding force data sample and the wavelet basis function as follows: ， In the formula, DWT F ( m , n ) represents the discrete wavelet transform signal processing process, < > and represent inner product operation and conjugate complex number respectively, F ( t ) represents the tangential grinding force data sample, is the discrete dyadic wavelet basis function, m represents the scale factor, n represents the displacement factor; Next, the projected data are projected onto the scaling function and the wavelet function. Specifically, the original tangential grinding force data samples are decomposed into low-frequency signals and high-frequency signals. The expressions of the low-frequency signals and the high-frequency signals are: ， ， In the formula, < > and represent inner product operation and conjugate complex number respectively, F ( t ) represents the original tangential grinding force signal, represents the decomposed low-frequency signal, represents the decomposed high-frequency signal, h m,n represents the low-pass filter coefficient, g m,n Represents the high-pass filter coefficients.

5. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on wavelet transform model as claimed in claim 1, characterized in that: The expression of the inverse transformation process of the wavelet transform in step 5 is: ， In the formula represents the low-frequency reconstructed signal, J represents the number of decompositions, h m,n Indicates m Second decomposition, n The low-pass filter coefficients.

6. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on the wavelet transform model according to any one of claims 1 to 5, characterized in that: On the timeline of the grinding process, there are: The first stage: the amplitude of the high-frequency data sample is relatively small and remains stable, indicating that the material is in the elastic deformation stage; The second stage: the amplitude of the high-frequency data sample increases relatively, and as the deformation continues, it shows an overall upward trend, which indicates that the material has entered the elastic-plastic deformation stage; The third stage: The amplitude of the high-frequency data sample suddenly increases sharply, indicating that the material has entered the stage of transition from plasticity to brittleness; The relative increase time point of the amplitude of the high-frequency data samples in the second stage is taken as the critical time point of the elastic-plastic transformation characteristics of the titanium-aluminum alloy material. The tangential grinding force and normal grinding force corresponding to the critical time point are the critical grinding forces of the elastic-plastic transformation. The time point of the sudden increase in the amplitude of the high-frequency data samples in the third stage is taken as the critical time point of the ductile-brittle transition characteristics of the titanium-aluminum alloy material, and the corresponding tangential grinding force and normal grinding force are the critical grinding forces of the ductile-brittle transition.

7. The method for calculating the elastic-plastic-brittle critical grinding force of titanium-aluminum alloy based on the wavelet transform model as claimed in claim 6 is characterized in that: It also includes the fourth stage when the amplitude of the high-frequency data sample no longer follows any obvious rules, indicating that the material has completely transformed into the brittle fracture removal stage. At this time, the grinding force corresponding to the time point when the amplitude no longer follows any obvious rules is the critical grinding force of complete brittle transformation.

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