A method for visualizing bending moment data of milling based on polar coordinates

Abstract

The application provides a kind of based on polar coordinate milling machining bending moment data visual expression method, by analyzing the bending moment signal in milling, the amplitude characteristics and tooth profile proportion characteristics extracted from the bending moment signal are input into the bending moment polar coordinate model for visual expression, and the bending moment time sequence model in the milling process is constructed by the time sequence superposition mode, so that the model can express the bending moment stress signal in time sequence, and clearly and stably depict the tool state.The method makes the bending moment polar coordinate model more stable by theoretical formula derivation, and the signal characteristics input into the model make the model more clearly and accurately express the characteristics of the real objective physical meaning contained in the processing signal data, which is beneficial to people's cognition of the situation in actual processing.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of graphical processing and analysis of mechanical processing data, and particularly relates to a method for visual expression of milling bending moment data based on polar coordinates. BACKGROUND

[0002] In the mechanical processing, the interaction between the tool and the workpiece is a fast and complex changing process, and the force change between them is the root of the change of other physical quantities. Collecting and analyzing the force of the tool can directly or indirectly deduce the actual processing conditions. When abnormal processing conditions such as workpiece deformation, unqualified processing quality, tool wear, tool chipping occur in the workpiece during processing, the force on the tool will also fluctuate. After preprocessing, the collected large data including normal processing and abnormal processing of the tool force are converted into samples and input into the neural network for learning. After learning, the model can even predict whether the next moment of work condition data is abnormal through existing data. If it is abnormal, it will immediately alarm and stop the operation of the machine tool, so that engineers can timely find and handle it, thereby avoiding the occurrence of abnormal processing conditions. The learning efficiency and prediction effect of the model are closely related to the samples input for learning, so it is of great significance to study the tool force signal in the processing.

[0003] In the mechanical processing, when using original time series data to analyze the tool state, relying only on manual experience for observation and judgment will have a large human error; the method of inputting the data into the neural network for learning is too dependent on the quality of the constructed model, and does not have general applicability.

[0004] In the collection of processing data, most sensors can collect data such as force, bending moment, vibration, temperature, current, pulse, angle, etc. in XYZ three-dimensional space coordinates, and perform data processing operations such as model construction and data analysis. The commonly used data processing methods are divided into two types. One is to construct the collected data visually, which is convenient for engineers to directly and intuitively observe and analyze the working condition data and processing status through manual methods. The other is to input the collected data into a network model through methods such as neural network and deep learning for supervised or unsupervised learning to realize simulation analysis and even prediction of the data. For example, the German Spike company inputs the collected bending moment X and bending moment Y data into a rectangular coordinate system for visual display to form a Spike bending moment model. By visualizing the "tool flower" shaped image, the tool wear, chipping and other states can be analyzed. However, since the Spike model uses data itself as the basis for model construction, the noise and packet loss problems existing in the data collection process will also affect the expression of the model, so the Spike model cannot clearly express the tool state in processing.

[0005] In contrast to the Spike bending moment model, which constructs a Cartesian coordinate system (bending moment X, bending moment Y) based on the signal data of bending moment X and bending moment Y, and then displays the data as a scatter plot, the Spike bending moment model suffers from several drawbacks. Because this model relies on the data itself as its foundation, and data acquisition can introduce noise and packet loss, the visualization is cluttered and incomplete, failing to accurately reflect changes in tool wear or clearly characterize the tool's state. Furthermore, the Spike model lacks temporal feature representation, failing to reflect the data's temporal sequence and hindering temporal logic analysis of the visualized model. Summary of the Invention

[0006] The technical problem solved by this invention is: in order to clearly characterize the features with real objective physical meaning contained in the collected machining data, and to express the objective physical meaning of the collected data, so that the data can be more descriptive of real machining when it is perceived by humans and learned by neural networks, this invention proposes a method for visualizing milling bending moment data based on polar coordinates. By inputting the collected and processed bending moment signal data into the constructed bending moment polar coordinate model for visualization, it can be used to analyze and judge the tool status and tool wear, and to understand the situation that occurs in actual machining by analyzing the results.

[0007] The technical solution of this invention is: a method for visualizing milling bending moment data based on polar coordinates, comprising the following steps:

[0008] Step 1: Construct a polar coordinate model of the bending moment of the full tooth signal data;

[0009]

[0010] In the formula: N represents the number of tool teeth, i represents the order of each single tooth signal within a single full-tooth signal data; A i For a single tooth signal data point within a single full-tooth signal data point, A represents the amplitude characteristics of each single-tooth signal data point, where A is [A1, A2, ..., A...]. N ], α i For a single full-tooth signal data set, α represents the tooth profile proportion of each single-tooth signal data set, where α is: [α1, α2, ..., α...]. N The tooth profile proportion feature refers to the proportion of tooth profile signal data within a single tooth signal data set to the total data.

[0011] Step 2: After acquiring the original bending moment signal data, extract the amplitude feature A and tooth profile ratio feature α of all full tooth signal data;

[0012] Step 3: The number of tool teeth N, and the amplitude characteristic A and the tooth profile ratio characteristic a obtained in step 2 are brought into the bending moment polar coordinate model of the full-tooth signal data constructed in step 1 to obtain the continuous bending moment polar coordinate model visualization expression of the single full-tooth signal data, and then the visualization expression is sequentially superimposed to realize the visualization expression of the milling machining bending moment data.

[0013] Further, in step 1, the following sub-steps are included:

[0014] Step 1.1: Analyze the original bending moment signal data, define the tooth profile signal data and the non-tooth profile signal data, and obtain the single-tooth signal data definition;

[0015] Step 1.2: Construct the bending moment polar coordinate model of the single-tooth signal data:

[0016] The single-tooth basic model is:

[0017] ρ=Asin(θ),0<θ<π (1-1)

[0018] Where the polar radius 0<ρ<A, A is the amplitude characteristic of the tooth profile signal data in the single-tooth signal data, which takes the maximum value in the single-tooth signal data;

[0019] Iterate formula (1-1) to obtain the single-tooth tooth profile signal data model:

[0020]

[0021] Where β is the polar angle value range variation coefficient, and N is the number of tool teeth;

[0022] Triangular transformation is performed on formula (1-2) to obtain

[0023]

[0024] Where θ α is the starting polar angle of the tooth profile signal in after introducing the non-tooth profile signal;

[0025] Step 1.3: N single-tooth signal data constitutes a full-tooth signal data, and the bending moment polar coordinate model of the full-tooth signal data is obtained according to the single-tooth tooth profile signal data model of formula (1-3).

[0026] Further, in step 1.1, the process of constructing the tooth profile signal data and the non-tooth profile signal data and obtaining the single-tooth signal data is as follows:

[0027] For the original bending moment signal data, the signal data generated when the tooth is cut into the workpiece is defined as the tooth profile signal data, and the data generated before and after the tooth is cut into the workpiece is defined as the non-tooth profile signal data;

[0028] The midpoint of the line connecting the maximum points of two adjacent tooth-shaped signal data is taken as the single-tooth signal data separation point; each pair of adjacent single-tooth signal data separation points divides a single-tooth signal data: each segment of non-tooth-shaped signal data is divided into two, and the part of two adjacent non-tooth-shaped signal data that is close to the middle tooth-shaped signal data and the tooth-shaped signal data it contains together form a single-tooth signal data.

[0029] Furthermore, step 2 includes the following sub-steps:

[0030] Step 2.1: Data Preprocessing: Based on vectors and formulas The bending moment X and bending moment Y in the original bending moment signal data are vector summed to obtain the bending moment vector sum. After filtering and noise reduction, the data is then interpolated to ensure the integrity of the data time sequence, resulting in complete time sequence bending moment vector sum signal data.

[0031] Step 2.2: Extract amplitude feature A: A is represented as [A1, A2, ..., A N A1 is the maximum point of a single tooth signal data in the complete time-series bending moment vector and signal data obtained in step 2.1, which serves as the starting point for data acquisition. The coordinate of A1 is x1. The data volume T of one single tooth signal data is then extended sequentially, and the extreme value error range (a, b) is set so that the maximum value range of the next single tooth is (x1+T+a, x1+T+b). Within this range, the maximum point is taken as A2, and its coordinate is x2. This process is iterated to obtain N amplitude features: [A1, A2, ..., A N ] and its corresponding coordinates;

[0032] Construct the coordinates of the amplitude characteristics of all full-tooth signal data as

[0033] P x : [[x1,x2,...,x N ],[x1,x2,...,x N ],[x1,x2,...,x N ],...];

[0034] The amplitude characteristics of all full-tooth signal data are constructed as follows:

[0035] P A : [[A1,A2,...,A N ],[A1,A2,...,A N ],[A1,A2,...,A N ],...];

[0036] Step 2.3: Extract the tooth profile proportion feature α: In a single full-tooth signal data set, compare the amount of tooth profile signal data in each single-tooth signal data set with the amount of single-tooth signal data to obtain the tooth profile proportion feature, and record it as α: [α1, α2, ..., α N ]; Construct the tooth profile proportion features of all full tooth signal data as

[0037] N α : [[α1,α2,...,α N ],[α1,α2,...,α N ],[α1,α2,...,α N ],...].

[0038] Furthermore, step 2.3 includes the following sub-steps:

[0039] Step 2.3.1: Divide the single-tooth signal data: After obtaining the coordinates of the amplitude features, calculate the midpoint of the line connecting adjacent coordinate points to obtain the dividing point of the single-tooth signal data; for every two adjacent dividing points of the single-tooth signal data, a start and end point of the single-tooth signal data is constructed, thus completing the division of the single-tooth signal data;

[0040] Step 2.3.2: Divide the tooth profile signal data, including:

[0041] Determine the starting point: Take sequential values ​​of the gradient changes of the single tooth signal data and compare them with the upper limit of the gradient threshold range until the value is greater than or equal to the upper limit of the gradient threshold range. When all gradient changes within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are greater than the upper limit of the gradient threshold range, set the coordinate point corresponding to this value as the starting point of the tooth profile signal.

[0042] Determine the termination point: Take the gradient values ​​of the single tooth signal data in reverse order until the value is less than or equal to the lower limit of the gradient threshold range. When all gradient values ​​within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are less than the lower limit of the gradient threshold range, the corresponding coordinate value is set as the termination point of the tooth profile signal.

[0043] Invention Effects

[0044] The technical advantages of this invention are as follows: This invention proposes a method for visualizing milling bending moment data based on polar coordinates. This method constructs a bending moment polar coordinate model, incorporates signal features extracted from bending moment signal data, and visualizes the bending moment polar coordinate model in milling. The model, displayed on the polar coordinate graph, resembles the "knife flower" pattern of the cutting edge, thus reflecting changes in the state of the corresponding teeth of the tool from the changes in the polar coordinate image. Therefore, the bending moment polar coordinate model in milling can not only express the bending moment force signal in milling in a time sequence but also reflect the tool wear, thereby achieving a clearer physical characterization of the tool state implied by the bending moment data. It is also more convenient for human visual recognition and computer image recognition, enabling the diagnosis and analysis of anomalies in the machining process data.

[0045] This method analyzes bending moment signals during milling, extracting amplitude and tooth profile characteristics from these signals and inputting them into a bending moment polar coordinate model for visualization. Furthermore, it constructs a bending moment time-series model during milling through temporal overlay, enabling the model to clearly and stably depict both the bending moment force signal and the tool state. The method's theoretical formula derivation enhances the stability of the constructed bending moment polar coordinate model, and the input of extracted signal features allows for a clearer and more accurate representation of the objective physical characteristics contained within the machining signal data, facilitating understanding of the actual machining process. Attached Figure Description

[0046] Figure 1 Bending moment data time series diagram

[0047] Figure 2 Logical mapping relationship of bending moment polar coordinate model for single-tooth signal data

[0048] Figure 3 Single-tooth signal data partitioning diagram

[0049] Figure 4 Tooth-shaped signal data partitioning diagram

[0050] Figure 5 Logic diagram of a method for visualizing milling bending moment data based on polar coordinates

[0051] Figure 6 Model Analysis Comparison Chart Detailed Implementation

[0052] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0053] See Figures 1-6 This embodiment proposes a method for visualizing milling bending moment data based on polar coordinates, including the following steps:

[0054] Step 1: Construct the polar coordinate model of bending moment

[0055] Step 1.1: Analyze the original bending moment signal data

[0056] The sensor that collects bending moment data is a sensor whose bending moment acquisition coordinate system is stationary relative to the spatial distribution of the tool holder. That is, the bending moment coordinate system constructed by the sensor collecting bending moments X and Y is stationary relative to the tool, and the bending moment signals measured by different teeth are expressed in different quadrants of the bending moment coordinate system. When the cutting teeth are subjected to milling force, due to the different positions of the teeth, the signals of bending moments X and Y monitored by the sensor have different signs. Figure 1 This section presents the bending moment X and Y diagrams and the corresponding bending moment vector sum diagram for a three-tooth end mill. From the bending moment vector sum diagram, it can be seen that each convex signal segment represents the signal data generated when the corresponding tooth of the cutter cuts the workpiece, collected by the sensor; this portion of the signal data is defined as tooth profile signal data. The portion of the tooth profile signal data that changes smoothly and approaches 0 represents the data generated before and after the corresponding tooth cuts the workpiece; this portion of the signal data is defined as non-tooth profile signal data. The midpoint of the line connecting the maximum points of every two adjacent tooth profile signal data segments is taken as the single-tooth signal data separator. Each pair of adjacent single-tooth signal data separators divides a single-tooth signal data segment, effectively splitting each segment of non-tooth profile signal data in two. The portion of two adjacent non-tooth profile signal data segments closest to the middle tooth profile signal data segment, along with the tooth profile signal data they contain, together constitute a single-tooth signal data segment.

[0057] Step 1.2: Construct the bending moment polar coordinate model of the single-tooth signal data:

[0058] To represent the bending moment force signal during milling in a time-series manner, and to characterize tool tooth splitting and wear, it is necessary to visualize a "tool tooth pattern" resembling the tool tooth profile through time-series iterations. Furthermore, according to Fourier's principle—any continuously measured time series or signal can be represented as an infinite superposition of sinusoidal signals of different frequencies—a polar coordinate bending moment model is constructed based on the mapping relationship between the sine function in the rectangular coordinate system and the polar coordinate system. The logical mapping relationship diagram for constructing the polar coordinate bending moment model of single-tooth signal data is shown below. Figure 2 .

[0059] In a Cartesian coordinate system, the standard sine function within a single period is y = sin(x), 0 < x < 2π. Its standard sine function in polar coordinates is ρ = sin(θ), 0 < θ < 2π. What needs to be visualized is the vector sum of bending moments X and Y in the machining data. This vector sum is positive; therefore, the basic model of a single tooth is set as follows:

[0060] ρ=Asin(θ),0<θ<π (1-1)

[0061] Where the polar diameter 0 < ρ < A, and A is the amplitude characteristic of the tooth profile signal data in the single tooth signal data, that is, the maximum value in the single tooth signal data.

[0062] Since a knife has multiple teeth, let's say the number of teeth is N. The polar coordinate system only extends to (0, 2π), so we need to represent all the teeth of the knife within (0, 2π). Therefore, we use iterative formula 1-1, assuming the single-tooth profile signal data model is:

[0063]

[0064] Where β is the coefficient for the variation of the polar angle in polar coordinates, that is, the polar angle varies from the range of (0,π) in Formula 1-1 to... When, the coefficient of change of the independent variable polar angle θ is obtained from have to

[0065] When the sensor's acquisition frequency and the machine tool spindle speed remain constant, the amount of single-tooth signal data remains constant. However, as machining progresses and the tool wears, the cutting edge wears, increasing the contact area between the cutting edge and the workpiece. This results in the sensor acquiring more signals of the cutting edge cutting the workpiece, meaning the amplitude and amount of tooth profile signal data increase. Therefore, the proportion of tooth profile signal data within the total single-tooth signal data can be used to express the tool wear condition, and this proportion is defined as the tooth profile proportion characteristic α. Figure 1As shown in the mid-bending moment vector sum, the tooth profile signal data is located in the middle of the single tooth signal data, and the non-tooth profile signal data is located on both sides of it. Therefore, the non-tooth profile signal data is expressed in polar coordinates. Introducing the tooth profile proportion feature α, a simple trigonometric function transformation according to Formula 1-2 yields Formula 1-3:

[0066]

[0067] Where θ α After introducing non-tooth-shaped signals, the tooth-shaped signals are in The starting polar angle is set, and after setting the non-tooth signal, the data volume on both sides of the tooth signal is equal and the value is 0. Therefore, the polar angle range of its tooth signal is... The polar angle range of non-tooth-shaped signals is Depend on have to At this time Substitute θ α have to

[0068] Step 1.3: Construct the bending moment polar coordinate model of the full tooth signal data:

[0069] The polar coordinate model of the entire tooth of the milling cutter during the cutting process is derived based on formulas 1-3:

[0070] If the number of teeth on the milling cutter is N, then N single-tooth signal data constitute a full-tooth signal data. From a full-tooth signal data, extract N consecutive amplitude features A: [A1, A2, ..., A...]. N This is to obtain the amplitude characteristics of the full tooth signal data, and to obtain the tooth profile proportion characteristic α of the full tooth signal data based on the corresponding position: [α1, α2, ..., α N ], and solve for the corresponding θ. α :[θ α1 ,θ α2 ,...,θ αN ] and β: [β1,β2,...,β N Therefore, the iterative formula is as follows:

[0071]

[0072] The simplified formulas of Equation 1-4 are as follows:

[0073]

[0074] In the formula, i represents the order of the single teeth of the cutting tool, i.e., i = 1, 2, ..., N.

[0075] coefficient of change and the initial polar angle Substituting into formulas 1-5, we obtain the polar coordinate model of the bending moment of the full tooth signal data:

[0076]

[0077] In the formula:

[0078] N - Number of teeth on the cutting tool

[0079] i — The order of each single-tooth signal within a single full-tooth signal data set.

[0080] A i —The amplitude characteristics of each single-tooth signal data within a single full-tooth signal data set, i.e., A: [A1, A2, ..., A N ]

[0081] α i —The tooth profile proportion of each single tooth signal data within a single full-tooth signal data, i.e., α: [α1, α2, ..., α N}

[0082] Step 2: Extraction of Data Features

[0083] Step 2.1: Data Preprocessing

[0084] After obtaining the original bending moment signal data, according to the vector sum formula The bending moments X and Y are vector summed to obtain their vector sum, which is then filtered and denoised. Null interpolation is then performed to ensure the integrity of the data timing sequence, resulting in complete timing vector sum signal data, which allows for the extraction of signal features based on timing.

[0085] Step 2.2: Extract amplitude feature A

[0086] To extract the amplitude of each single-tooth signal data, it is necessary to locate it, which means obtaining the interval data size of the amplitude characteristics of adjacent single-tooth signal data in the time-series coordinate system. Since the data size of each single-tooth signal data is equal after the machine tool spindle speed and sensor acquisition frequency are determined during machining, that is, the interval data size of the amplitude characteristics of adjacent single-tooth signal data in the time-series coordinate system is fixed and equal to the data size of each single-tooth signal data, the data size of the single-tooth signal is calculated based on the machine tool spindle speed and sensor acquisition frequency during machining.

[0087]

[0088] T – Data volume of a single-tooth signal

[0089] n—spindle speed, in r / min

[0090] f—Sensor acquisition frequency, Hz

[0091] N - Number of teeth on the cutting tool

[0092] Since T is not necessarily an integer in the data calculation, and the spindle speed of the machine tool is not necessarily constant or the sensor acquisition frequency fluctuates, causing the amount of single tooth signal data acquired to change, it is necessary to set an extreme value error range (a, b).

[0093] In the complete time-series bending moment vector and signal data, a single tooth signal data point is set as the starting point for data acquisition. Its maximum value point is taken as A1, and its coordinate is taken as x1. The data volume of the next single tooth signal data point is then extended, and an extreme value error range is set, so that the maximum value range of the next single tooth signal data point is (x1+T+a, x1+T+b). Within this range, its maximum value point is taken as A2, and its coordinate is taken as x2. This process is iterated until N amplitude features are obtained, resulting in the amplitude feature A of the full tooth signal data: [A1, A2, ..., A...]. N The amplitude feature A and its corresponding coordinates are extracted for the next full-tooth signal data, and so on, until the bending moment vector and signal data of the complete time series are obtained.

[0094] Construct the coordinates of the amplitude characteristics of all full-tooth signal data as

[0095] P x : [[x1, x2, ..., x N ],[x1,x2,...,x N ],[x1,x2,...,x N ], ...], so as to support the extraction of the shape proportion feature α;

[0096] The amplitude characteristics of all full-tooth signal data are constructed as follows:

[0097] P A : [[A1, A2, ..., A N ],[A1,A2,...,A N ],[A1,A2,...,A N ], ...], to facilitate the construction of polar coordinate models of bending moments in milling processes;

[0098] Step 2.3 Extract the tooth profile proportion feature α

[0099] To extract the tooth profile proportion feature of each single-tooth signal data, it is first necessary to divide the single-tooth signal data and the tooth profile signal data, that is, to obtain the coordinates of the start and end points of each single-tooth signal data and its tooth profile signal data. After obtaining the coordinates of the amplitude feature, the midpoint of the line connecting adjacent coordinate points can be calculated to obtain the dividing point of the single-tooth signal data. Each pair of adjacent single-tooth signal data dividing points constitutes the start and end point of a single-tooth signal data, thus completing the division of the single-tooth signal data. The operation process is as follows: Figure 3 As shown. Therefore, according to P x Divide the single-tooth signal data into each full-tooth signal data.

[0100] Within each single-tooth signal data set, the tooth-shaped signal data is a convex signal data, centered in position, while the non-tooth-shaped signal data changes gradually, approaching zero, and is distributed on both sides of the tooth-shaped signal data. Therefore, the gradient of the data changes within the single-tooth signal data is used as the basis for dividing the tooth-shaped and non-tooth-shaped signals. Gradient calculations are performed on all single-tooth signal data, and a gradient threshold range is set. The gradient of the single-tooth signal data is sequentially taken and compared with the upper limit of the gradient threshold range until its value is greater than or equal to the upper limit of the gradient threshold range. When all gradient values ​​within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are greater than the upper limit of the gradient threshold range, the coordinate point corresponding to this value is set as the starting point of the tooth-shaped signal. The gradient of the single-tooth signal data is taken in reverse order until its value is less than or equal to the lower limit of the gradient threshold range. When all gradient values ​​within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are less than the lower limit of the gradient threshold range, the coordinate point corresponding to this value is set as the ending point of the tooth-shaped signal. This method extracts the starting and ending points of the tooth-shaped signal data, thus completing the division of the tooth-shaped signal data. The operation process is as follows: Figure 4 As shown.

[0101] In a single full-tooth signal data set, based on the coordinates of the recorded amplitude characteristics, the data volume of the tooth profile signal data in each single-tooth signal data set is compared with the data volume of the single-tooth signal data set to obtain the tooth profile proportion characteristic, which is recorded as α: [α1, α2, ..., α N ], construct N from the tooth profile proportion features of all full tooth signal data. α : [[α1, α2, ..., α N ], [α1, α2, ..., α N ], [α1, α2, ..., α N [, ...], to facilitate the construction of polar coordinate models of bending moments in milling processes.

[0102] The same data feature extraction method is also applicable to milling with variable spindle speed. The original data can be divided and calibrated into data segments for different spindle speed stages, and the amplitude feature A and tooth profile ratio feature α can be extracted for different data segments.

[0103] Step 3: Constructing the polar coordinate model of bending moment in milling machining

[0104] Step 3.1 Constructing a polar coordinate model of bending moment for a single full-tooth signal data

[0105] The number of tool teeth N and the amplitude characteristics A of the extracted single full-tooth signal data are: [A1,A2,...,A1]. N ] and tooth profile proportion feature α: [α1, α2, ..., α N By applying formulas 1-6, the bending moment polar coordinate model of a single full-tooth signal data can be constructed.

[0106] Step 3.2: Construct a visual representation of the polar coordinate model of bending moment in milling.

[0107] Based on the amplitude characteristics of all full-tooth signal data, P A The tooth profile proportion characteristic is P α Furthermore, the bending moment polar coordinate model of a single full tooth signal data can be constructed, and the bending moment polar coordinate model of a continuous single full tooth signal data can be sequentially superimposed to realize the visualization of the bending moment polar coordinate model in milling.

[0108] The present invention will now be described in detail with reference to specific embodiments.

[0109] Based on the experimental data obtained from the machining process, the above-mentioned implementation scheme was carried out in detail. The experimental data consisted of bending moment data collected by a sensor whose bending moment acquisition coordinate system was stationary relative to the spatial distribution of the tool holder during milling. The number of milling cutter teeth was N=3, the spindle speed of the machining tool was n=1500rad / min, and the sensor acquisition frequency was f=2.5kHz.

[0110] Step 1: Establish the bending moment model

[0111] Since N = 3, and combining with expression (1-6), the bending moment polar coordinate model of the full tooth signal data is obtained as follows:

[0112]

[0113] Step 2: Extract data features

[0114] The bending moment signals X and Y in the original data are vector summed. Using the principle of polynomial least squares, the data are filtered and denoised using a Savitzky-Golay filter. The missing values ​​are then filled by arithmetic sequence interpolation of the first and last data to obtain the complete time-series bending moment vector sum signal data.

[0115] Calculate the data volume of a single-tooth data signal according to formula 1-7:

[0116]

[0117] Following step 2.2, iterate through the data until all bending moment vectors and signal data for the complete time series are obtained, and acquire the amplitude characteristic P. A : [[A1, A2, ..., A N ],[A1,A2,...,A N ],[A1,A2,...,A N [, ...] and the coordinates P of the amplitude characteristic x : [[x1, x2, ..., x N ],[x1,x2,...,x N ],[x1,x2,...,x N ], ...].

[0118] Based on step 2.3, combined with the already obtained P x The single-tooth signal data and tooth profile signal data are separated, and the tooth profile proportion feature P is obtained by using the data change gradient as a discriminant condition. α : [[α1, α2, ..., α N ], [α1, α2, ..., α N ], [α1, α2, ..., α N ], ...

[0119] Step 3: Construct a visual representation of the bending moment polar coordinate model in milling.

[0120] The obtained P A With P α Based on step 3, the model is input and iterated and accumulated in a visual manner to draw a polar coordinate model representation of bending moment in milling with a "knife flower" shape.

[0121] Comparative analysis with the Spike model

[0122] Using data from different stages of milling with a milling cutter, the Spike model and the polar coordinate model of bending moment in milling were constructed respectively. Figure 6 .

[0123] The first row shows the visualization from the Spike model, and the second row shows the visualization from the bending moment polar coordinate model during milling. The scale ranges of both images are identical and remain constant. Comparative analysis reveals that because the Spike model uses the data itself as its foundation, its data acquisition process introduces noise and packet loss, leading to incomplete and unstable visualizations that fail to clearly represent the state of each tool tooth. In contrast, the bending moment polar coordinate model provides a complete and stable overall representation. Its clear iterative representation of each tool tooth allows for a comprehensive depiction of the tool's overall state, facilitating the analysis of features such as tool wear. Furthermore, because the Spike model relies on a scattered Cartesian coordinate system, it can only express the spatial distribution of bending moment data and cannot analyze the temporal sequence of data collected during machining. The bending moment polar coordinate model, based on the temporal iteration of the polar coordinate system, not only expresses the tool state but also allows for analysis of the temporal sequence of tool state changes through its iteration order.

[0124] In summary, this invention utilizes the mapping relationship between rectangular and polar coordinate systems to derive a polar coordinate model of bending moment by analyzing bending moment signal data collected by sensors during milling. This model combines the expression of bending moment force with characteristic signals reflecting the wear state of the milling cutter. The extracted characteristic signals are then fed into this model, and a temporal model of bending moment during the milling process is constructed through temporal superposition. This model not only expresses the bending moment force signal in a temporal sequence but also clearly and stably depicts the tool state. Specifically, as the tool wears, the proportion of tooth profile signal within a single tooth increases, causing the "tool pattern" on the polar coordinate image to expand. Therefore, this invention, through image representation, not only expresses the temporal bending moment signal but also reflects the tool wear condition. As an objective physical representation of the milling cutter in milling, it facilitates the understanding of tool wear during actual machining.

Claims

1. A method for visualizing milling bending moment data based on polar coordinates, characterized in that, Includes the following steps: Step 1: Construct a polar coordinate model of the bending moment of the full tooth signal data; In the formula: This is expressed as the number of teeth on the cutting tool. This represents the order of each single-tooth signal within a single full-tooth signal data set. For a single tooth signal data point within a single full-tooth signal data point, the amplitude characteristics of each single-tooth signal data point are... , This refers to the tooth profile proportion of each single tooth signal data point within a single full-tooth signal data set. The tooth profile proportion feature refers to the proportion of tooth profile signal data within a single tooth signal data set to the total data. Step 2: After acquiring the raw bending moment signal data, extract the amplitude characteristics of all full-tooth signal data. and tooth profile proportion characteristics ; Includes the following sub-steps: Step 2.1: Data Preprocessing: Based on vectors and formulas The bending moment X and bending moment Y in the original bending moment signal data are vector summed to obtain the bending moment vector sum. After filtering and noise reduction, the data is then interpolated to ensure the integrity of the data time sequence, resulting in complete time sequence bending moment vector sum signal data. Step 2.2: Extract amplitude features : Represented as ; The maximum point of a single-tooth signal data, which serves as the starting point for data acquisition, is the bending moment vector and signal data obtained in the complete time series from step 2.

1. The coordinates are The data volume T of a single-tooth signal is then added, and an extreme value error range is set. This makes the range of the maximum value of the next single tooth be [value missing]. Within this range, take its maximum point as Take its coordinates as This process is iterated to obtain N amplitude features: and its corresponding coordinates; construct the coordinates of the amplitude characteristics of all full-tooth signal data as ; The amplitude characteristics of all full-tooth signal data are constructed as follows: ; Step 2.3: Extract tooth profile proportion features In a single full-tooth signal dataset, the amount of tooth profile signal data in each single-tooth signal dataset is compared to the amount of single-tooth signal data to obtain the tooth profile proportion feature, which is then recorded as follows: ; Construct the tooth profile proportion features of all full tooth signal data as ; Step 3: Adjust the number of teeth on the cutting tool and the amplitude characteristics obtained in step 2 and tooth profile proportion characteristics By inputting the bending moment polar coordinate model of the full tooth signal data constructed in step 1, a visual representation of the bending moment polar coordinate model of a continuous single full tooth signal data is obtained. Then, the visual representations are sequentially superimposed to realize the visual representation of the milling bending moment data.

2. The method for visualizing milling bending moment data based on polar coordinates as described in claim 1, characterized in that, Step 1 includes the following sub-steps: Step 1.1: Analyze the original bending moment signal data, define the tooth profile signal data and non-tooth profile signal data, and obtain the definition of single tooth signal data; Step 1.2: Construct the bending moment polar coordinate model of the single-tooth signal data: The basic model of a single tooth is: （1-1） Among them, the polar diameter , To determine the amplitude characteristics of the tooth profile signal data in the single-tooth signal data, the maximum value in the single-tooth signal data is taken. The iterative formula (1-1) yields the single-tooth profile signal data model as follows: （1-2） in is the coefficient for the range of polar angle values ​​in polar coordinates, and N is the number of tool teeth; Performing trigonometric transformations on formula (1-2), we obtain (1-3) in After introducing non-tooth-shaped signals, the tooth-shaped signals are... The initial polar angle in; Step 1.3: N single-tooth signal data constitute a full-tooth signal data. Based on the single-tooth profile signal data model of formula (1-3), the bending moment polar coordinate model of the full-tooth signal data is obtained.

3. The method for visualizing milling bending moment data based on polar coordinates as described in claim 2, characterized in that, In step 1.1, the process of defining tooth-shaped signal data and non-tooth-shaped signal data, and obtaining single-tooth signal data, is as follows: In the original bending moment signal data, the signal data generated when the tooth cuts into the workpiece is defined as tooth profile signal data, and the data generated before and after the tooth cuts into the workpiece is defined as non-tooth profile signal data. The midpoint of the line connecting the maximum points of two adjacent tooth-shaped signal data is taken as the single-tooth signal data separation point; each pair of adjacent single-tooth signal data separation points divides a single-tooth signal data: each segment of non-tooth-shaped signal data is divided into two, and the part of two adjacent non-tooth-shaped signal data that is close to the middle tooth-shaped signal data and the tooth-shaped signal data it contains together form a single-tooth signal data.

4. The method for visualizing milling bending moment data based on polar coordinates as described in claim 1, characterized in that, Step 2.3 includes the following sub-steps: Step 2.3.1: Divide the single-tooth signal data: After obtaining the coordinates of the amplitude features, calculate the midpoint of the line connecting adjacent coordinate points to obtain the dividing point of the single-tooth signal data; for every two adjacent dividing points of the single-tooth signal data, a start and end point of the single-tooth signal data is constructed, thus completing the division of the single-tooth signal data; Step 2.3.2: Divide the tooth profile signal data, including: Determine the starting point: Take sequential values ​​of the gradient changes of the single tooth signal data and compare them with the upper limit of the gradient threshold range until the value is greater than or equal to the upper limit of the gradient threshold range. When all gradient changes within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are greater than the upper limit of the gradient threshold range, set the coordinate point corresponding to this value as the starting point of the tooth profile signal. Determine the termination point: Take the gradient values ​​of the single tooth signal data in reverse order until the value is less than or equal to the lower limit of the gradient threshold range. When all gradient values ​​within the range from the coordinate point corresponding to this value to the coordinate point of the tooth amplitude are less than the lower limit of the gradient threshold range, the corresponding coordinate value is set as the termination point of the tooth profile signal.

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