Cutting parameter driven milling chip 3D geometry modeling and simulation method and system

Abstract

The present invention discloses a cutting parameter-driven three-dimensional geometric modeling and simulation method and system for milling chips, which relates to the technical field of geometric modeling and simulation of milling chips on CNC milling machines. First, tool geometric parameters and milling cutting parameters are obtained. The tool geometric parameters include the number of milling cutter teeth, the milling cutter radius, and the cutting edge helix angle. The milling cutting parameters include the tool feed rate, the spindle speed, the cutting width, the cutting depth, etc.; based on the tool geometric parameters and the milling cutting parameters, the outer shape geometric parameters of the milling chips at the time of breaking are calculated; based on the outer shape geometric parameters, prediction simulation of the chip shape and dynamic real-time three-dimensional simulation of the chip shape are performed. The present invention can perform more comprehensive geometric modeling of the deformed shape of chips that break during the milling process, which is used for prediction and simulation of the shape of milling chips. At the same time, it can also realize dynamic real-time high-fidelity three-dimensional simulation of the milling chip shape, providing a reference basis for process designers.

Description

Technical Field

[0001] The present invention relates to the technical field of geometric modeling and simulation of milling chips of CNC milling machines, and more particularly to a cutting parameter-driven three-dimensional geometric modeling and simulation method and system for milling chips. Background Art

[0002] Milling is a key component manufacturing technology in the machining industry. As a subtractive machining process, milling removes material from a workpiece to produce a component with a specified shape and precision. When a milling cutter removes material, friction between the cutter's cutting edge and the workpiece creates elastic-plastic slip and deformation in the cut metal layer, generating chips. During milling, if process parameters are poorly planned, the chip shape can wrap around the cutter. This wrapping can cause machine downtime, tool wear, and process interruptions. Especially during finishing operations, the generated chips can rub against the finished workpiece surface, leading to reduced surface quality, component scrap, and low yield rates. Therefore, accurately predicting the chip shape at break during milling is crucial for improving machining efficiency, extending tool life, and ensuring workpiece quality. Ideally, broken chips should be easy to clean, avoid wrapping around the tool or workpiece, and not disrupt the machining process or pose safety risks.

[0003] In the prior art, research and patents on the prediction of broken chip shape mainly involve turning, gear hobbing, grinding, and broaching. There is less research on predicting chip shape during milling. Existing milling research only predicts the undeformed shape of milling chips and, in turn, the cutting forces during the cutting process, rather than the deformed shape of the chips when they break and fly out. The only predictions of broken chips during milling only predict and calculate some of the geometric parameters of the broken chips, such as chip width. On the other hand, the current simulation of chip shape is still limited to three-dimensional simulation of static parameters, without integrating real-time feedback of physical information for information-physics fusion simulation to achieve real-time dynamic simulation of broken chips.

[0004] Therefore, how to comprehensively and accurately predict the geometric shape of broken chips and perform dynamic three-dimensional simulation is an urgent problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a cutting parameter-driven three-dimensional geometric modeling and simulation method and system for milling chips, which predicts and simulates the broken shape of the chips during processing based on the tool geometric parameters and milling cutting parameters, thereby ensuring that the broken chips generated during the milling process will not entangle the tool, scratch the workpiece surface, etc., obtain reasonable cutting processing parameters, and improve the production efficiency and processing quality of component milling.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A cutting parameter-driven three-dimensional geometric modeling and simulation method for milling chips includes the following steps:

[0008] Step S1, obtaining tool geometric parameters according to tool model;

[0009] Step S2, obtaining milling cutting parameters;

[0010] Step S3, determining the geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters;

[0011] Step S4: performing three-dimensional geometric modeling and simulation on the chip shape according to the geometric parameters of the chip shape when it breaks during milling.

[0012] Optionally, in step S1, the specific method for obtaining the tool geometric parameters according to the tool model is:

[0013] Step S11, constructing a milling cutter parameter database, wherein the primary key of the milling cutter parameter database is the cutter model, and the data segment is the cutter geometric parameters, including the number of cutter teeth, the cutter radius, and the cutting edge helix angle;

[0014] Step S12: Obtain corresponding tool geometric parameters from the milling cutter parameter database according to the tool model.

[0015] Optionally, in step S2, the method for obtaining the milling cutting parameters is:

[0016] Get the NC code of the milling process;

[0017] The NC code is parsed to obtain the tool feed speed and spindle speed of the current machining process, and the cutting width and cutting depth are determined based on the tool motion path information in the NC code.

[0018] Optionally, in step S2, the method for obtaining the milling cutting parameters is:

[0019] According to the real-time detection information of the machine tool's encoding sensor and preset supplementary parameters, the real-time position of the milling machine, spindle speed, tool feed information, cutting width, and cutting depth are determined. The tool feed information includes tool position and tool feed speed.

[0020] Optionally, in step S3, the geometric parameters of the milling chip when it breaks include the maximum chip thickness, chip width, chip length, chip upper curvature, chip lateral curvature, and chip outflow angle.

[0021] Optionally, step S3 specifically includes:

[0022] Step S31, calculating the maximum thickness of the chips:

[0023] If the cutting width a e Greater than the milling cutter radius R, the maximum chip thickness h max Equal to the feed per tooth f;

[0024] If the cutting width a e Smaller than the milling cutter radius R, the maximum chip thickness h max for:

[0025]

[0026] Step S32, calculating chip width:

[0027] If the cutting width a e If it is greater than the milling cutter radius R, the chip width is the maximum chip width:

[0028] L max =a p sinα;

[0029] Among them, a p Indicates the cutting depth and the helix angle of the cutting edge;

[0030] Otherwise, the chip width L is calculated as:

[0031]

[0032] Wherein, the contact angle θ is:

[0033]

[0034] Step S33, calculating chip length:

[0035]

[0036] Wherein, Ls represents the chip length;

[0037] Step S34, calculating the chip curling rate:

[0038] The chip curling curvature and curling radius are in an inverse relationship, and the curling radius is:

[0039]

[0040] Where l represents the contact length of the chip, h represents the distance from the cutting plane of the tool face to the perpendicular line of the contact point between the chip and the tool, and w represents the distance from the tool tip to the cutting plane. The curling rate of the chip is

[0041] Step S35: Calculate the transverse curvature of the chip:

[0042] The transverse curvature of the chip and the transverse curling radius are inversely proportional. The transverse curling radius R cr The expression is:

[0043]

[0044] in, represents the lateral curvature of the chip;

[0045] Step S36: Calculate the chip outflow angle:

[0046]

[0047] Where, represents the chip outflow angle, AB=a p / sinα,AC=f.

[0048] Optionally, in step S4, three-dimensional geometric modeling and simulation of the broken chip shape are performed to specifically realize two functions, namely, a pre-processing simulation function and a real-time monitoring function during processing:

[0049] The pre-processing simulation function is to display the predicted milling chip shape in three dimensions according to the geometric parameters of the milling chip when it breaks;

[0050] The real-time monitoring function during machining refers to the dynamic three-dimensional display of the milling chip profile based on the real-time tool feed information obtained from the encoder coding information.

[0051] Optionally, during the three-dimensional geometric modeling and simulation of the chip shape, the helix angle increment for drawing the chip is adjusted, thereby changing the number of discrete triangular facets to achieve a preset three-dimensional display accuracy requirement.

[0052] A cutting parameter-driven milling chip three-dimensional geometric modeling and simulation system, comprising:

[0053] Tool geometry parameter extraction module, used to obtain tool geometry parameters based on tool model;

[0054] Cutting parameter extraction module, used to obtain milling cutting parameters;

[0055] a chip shape geometric parameter calculation module, for determining the shape geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters;

[0056] The three-dimensional display module is used to perform three-dimensional geometric modeling and simulation of the chip shape when it breaks according to the geometric parameters of the chip shape when it breaks.

[0057] From the above technical solutions, it can be seen that the present invention provides a cutting parameter-driven three-dimensional geometric modeling and simulation method and system for milling chips, which has the following beneficial effects compared with the prior art:

[0058] (1) The present invention supports the selection and addition of milling cutters with different geometric parameters from a milling cutter parameter database, and the selection of corresponding milling cutter models and milling cutting parameters. Based on the system and method of the present invention, the geometric parameters of the chip when it breaks, such as thickness, width, and length, can be automatically calculated;

[0059] (2) A three-dimensional simulation display algorithm for chips is implemented based on the geometric parameters of milling chips, so that the operator can directly determine whether the broken chips are of a reasonable shape through the three-dimensional display of the chips;

[0060] (3) It can not only be used to predict the chip shape before milling, but also can be combined with sensor information to realize the dynamic display of chips during the milling process, so that high-speed chips that were originally difficult to observe clearly can be displayed in three dimensions;

[0061] (4) The present invention has decision-making guidance significance for selecting appropriate tool geometric parameters and milling cutting parameters, so that in the actual milling process, the phenomena of chips wrapping around the tool, machine tool shutdown, and scratching the workpiece surface are avoided, thereby improving the milling efficiency of the workpiece and ensuring operational safety and workpiece surface quality.

[0062] In summary, this invention enables more comprehensive geometric parameter modeling of the deformed shape of chips that break during milling, enabling prediction of milling chip shape. Furthermore, by integrating sensor information from the machining process, dynamic, real-time, high-fidelity 3D simulation of milling chip shape is achieved, enabling production personnel to determine whether cutting parameters are appropriate and whether there will be entanglement with the tool or scratching of the workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0064] Figure 1 Schematic diagram for calculating the maximum thickness of milling chips;

[0065] Figure 2 Schematic diagram for calculating chip width in milling;

[0066] Figure 3 Schematic diagram for calculating the curling rate of milling chips;

[0067] Figure 4 Schematic diagram for calculating chip outflow angle in milling;

[0068] Figure 5 Schematic diagram showing three-dimensional simulation of milling chips;

[0069] Figure 6 A schematic diagram of the dynamic 3D simulation display in milling process for predicting the shape of broken chips;

[0070] Figure 7 Schematic diagram of the principle of the method of the present invention;

[0071] Figure 8 Schematic diagram of the system module of the present invention. DETAILED DESCRIPTION

[0072] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0073] Example 1

[0074] The embodiment of the present invention discloses a cutting parameter driven milling chip three-dimensional geometric modeling and simulation method, see Figure 7 , including the following steps:

[0075] Step S1: Obtain tool geometric parameters based on tool model. This specifically includes the following two steps:

[0076] Step S11: Constructing a milling cutter parameter database for milling cutters of milling type. The primary key of the milling cutter parameter database is the cutter model, and the data segment is the cutter geometric parameters, including the number of cutter teeth, cutter radius, cutting edge helix angle, cutter material, etc.

[0077] Step S12: Acquire corresponding tool geometric parameters from the milling cutter parameter database according to the currently used tool model.

[0078] Step S2: obtaining milling cutting parameters during the milling process. This mainly includes the following two steps:

[0079] Step S21, obtain the NC code of the milling process; construct an NC code parsing function module for the milling cutting parameters, parse the NC code, automatically obtain the tool feed speed and spindle speed of the current processing step, and determine the cutting width (side cutting amount) and cutting depth based on the tool motion path information in the NC code.

[0080] Step S22, construct a sensor data analysis function module for milling cutting parameters, and determine the real-time position of the milling machine, spindle speed, tool feed information, cutting width, and cutting depth based on the real-time detection information of the machine tool's encoding sensor (including spindle speed, moving axis position information) and preset supplementary parameters. The tool feed information includes tool position and tool feed speed.

[0081] The parameters acquired in step S21 are static parameters, while the parameters acquired in step S22 are dynamic parameters that change in real time, providing the basis for subsequent dynamic simulation. Step S21 is a general method that can stably acquire parameters. Parameter acquisition in step S22 requires the CNC system to support data communication capabilities.

[0082] Step S3: Determine the geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters, including the maximum chip thickness, chip width, chip length, chip curling rate, chip transverse curvature, and chip outflow angle. The step of calculating the geometric parameters of the milling chip when it breaks includes:

[0083] Step S31, calculating the maximum thickness of the chips:

[0084] The maximum chip thickness is related to the milling cutter radius, spindle speed, tool feed rate, and cutting width.

[0085] See also Figure 1 The principle shown, if the cutting width a e Greater than the cutter radius R, the maximum chip thickness h max Equal to the feed per tooth f;

[0086] If the cutting width ae If it is smaller than the milling cutter radius R, the maximum chip thickness h max for:

[0087]

[0088] Step S32, calculating chip width:

[0089] The milling chip width is related to the milling cutter radius, cutting width, and cutting edge helix angle, such as Figure 2 As shown, the cutting width is the contact length L between the main cutting edge of the milling cutter and the cutting layer of the workpiece. The contact length L between the main cutting edge and the workpiece is related to the contact angle θ.

[0090] If the cutting width a e If it is greater than the milling cutter radius R, the chip width is the maximum chip width:

[0091] L max =a p sinα;

[0092] Among them, a p Indicates the cutting depth and the helix angle of the cutting edge;

[0093] The calculation formula for chip width L under normal circumstances is:

[0094]

[0095] Wherein, the contact angle θ is:

[0096]

[0097] Step S33, calculating chip length:

[0098] The chip length is related to the milling cutter radius, cutting width, and cutting edge helix angle. The chip length Ls is calculated according to the helix length. The calculation formula is:

[0099]

[0100] Wherein, Ls represents the chip length;

[0101] Step S34, calculating the chip curling rate:

[0102] The chip curling rate is related to the contact length l between the tool face and the chip, the distance h from the tool face cutting plane to the perpendicular line of the chip and tool contact point, and the distance w from the tool face tip to the cutting plane. Figure 3 As shown, the chip curling curvature and the curling radius are in an inverse relationship, and the curling radius is:

[0103]

[0104] The curling rate of the chip is

[0105] Step S35: Calculate the transverse curvature of the chip:

[0106] The transverse curvature of the chip is related to the chip thickness and chip width. The transverse curvature of the chip and the transverse curling radius are inversely proportional. The transverse curling radius R cr The expression is:

[0107]

[0108] in, represents the lateral curvature of the chip;

[0109] Step S36: Calculate the chip outflow angle:

[0110] The chip flow angle is related to the cutting depth, cutting edge helix angle, and tool feed speed. According to the definition of equivalent cutting edge: the line connecting the two endpoints of the intersection of the main cutting edge actually involved in cutting and the surface to be machined and the intersection of the secondary cutting edge and the machined surface projected on the base plane, such as Figure 4 As shown, the angle CBA is the required chip flow angle, and the calculation formula is:

[0111]

[0112] Where, represents the chip outflow angle, AB=a p / sinα,AC=f.

[0113] Step S4: Based on the geometric parameters of the milling chip when it breaks, perform three-dimensional geometric modeling and simulation on the chip shape. The three-dimensional geometric modeling and simulation of the chip shape specifically realizes two functions, namely, pre-processing simulation function and real-time monitoring function during processing:

[0114] (1) The pre-processing simulation function is to display the predicted milling chip shape in three dimensions based on the geometric parameters of the milling chip when it breaks;

[0115] (2) The real-time monitoring function during processing refers to the dynamic three-dimensional display of the milling chip shape based on the real-time tool feed information obtained from the encoder encoding information of the encoding sensor in step S22. The encoding sensor includes an encoder and a sensor.

[0116] In the process of 3D geometric modeling and simulation of chip shape, the chip 3D display accuracy can be adjusted by adjusting the spiral angle increment of the chip drawing and then changing the number of discrete triangles. Figure 5As shown, the entire chip is discretized into triangular facets, which are generated by spiraling around the axis through the four vertices of the initial cross-section rectangle. The number of triangular facets can be controlled by controlling the rotation angle increment, thereby changing the display accuracy of the chip.

[0117] Therefore, the three-dimensional simulation function of the present invention can not only predict the chip shape before the actual milling process, but also display the movement of the chip following the milling cutter in real time according to the sensor information during the machining process, such as Figure 6 As shown in the figure, the physical information of the tool, such as position and speed, is acquired in real time by means of a coding sensor, so that the broken chip shape can be dynamically calculated and displayed in three dimensions.

[0118] Example 2

[0119] Based on the above-mentioned Example 1, specific example parameters are further listed. In this embodiment, the milling cutter radius is 8 mm, the number of teeth is 4, the cutting edge helix angle is 60 degrees, the tool feed speed is 200 mm / min, the spindle speed is 600 r / min, the cutting width is 5 mm, the cutting depth is 5 mm, the contact length between the blade and the chip is 1 mm, the distance from the blade tip to the cutting plane is 3 mm, and the distance from the blade cutting plane to the perpendicular line between the chip and the tool contact point is 3 mm. According to the method of the present invention, the geometric parameters of the broken chip are calculated, and the chip thickness is 0.08 mm, the chip width is 5.8 mm, the chip deflection angle is 59.9 degrees, the chip spiral length is 10.9 mm, the upper curl radius is 2.2 mm, the horizontal curl radius is 3.8 mm, and the chip outflow angle is 0.7 degrees.

[0120] Regarding the construction of the three-dimensional model, any geometric graphics library can be used to realize the construction of the three-dimensional model. Figure 5 The model in the figure is constructed using the open source graphics library OpenCasCade.

[0121] Example 3

[0122] This embodiment discloses a cutting parameter driven milling chip three-dimensional geometric modeling and simulation system, see Figure 8 ,include:

[0123] Tool geometry parameter extraction module, used to obtain tool geometry parameters based on tool model;

[0124] Cutting parameter extraction module, used to obtain milling cutting parameters;

[0125] a chip shape geometric parameter calculation module, for determining the shape geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters;

[0126] The three-dimensional display module is used to perform three-dimensional geometric modeling and simulation of the chip shape when it breaks according to the geometric parameters of the chip shape when it breaks.

[0127] As for the system module disclosed in this embodiment 3, since it corresponds to the method disclosed in embodiment 1, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0128] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0129] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A cutting parameter driven milling chip three-dimensional geometric modeling and simulation method, characterized in that: The following steps are involved: Step S1, obtaining tool geometric parameters according to tool model; Step S2, obtaining milling cutting parameters; Step S3, determining the geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters, specifically comprising: Step S31, calculate the maximum thickness of the chip: if the cutting width a e Greater than the milling cutter radius R, the maximum chip thickness h max Equal to the feed per tooth f; if the cutting width a e Smaller than the milling cutter radius R, the maximum chip thickness h max for: Step S32, calculate the chip width: if the cutting width a e If it is greater than the milling cutter radius R, the chip width is the maximum chip width: L max =a p / sinα; Among them, a p represents the cutting depth, and α represents the cutting edge helix angle; Otherwise, the chip width L is calculated as: Step S33, calculating chip length: Wherein, Ls represents the chip length; Step S34, calculating the chip curling rate: the chip curling rate and the curling radius are inversely proportional, and the curling radius is: Where l represents the contact length of the chip, h represents the distance from the cutting plane of the tool face to the perpendicular line of the contact point between the chip and the tool, and w represents the distance from the tool tip to the cutting plane. The curling rate of the chip is Step S35, calculate the transverse curvature of the chip: the transverse curvature of the chip and the transverse curling radius are inversely proportional, and the transverse curling radius R cr The expression is: in, represents the lateral curvature of the chip; Step S36: Calculate the chip outflow angle: Where η represents the chip outflow angle, AB=a p / sinα, AC=f; Step S4: performing three-dimensional geometric modeling and simulation on the chip shape according to the geometric parameters of the chip shape when it breaks during milling.

2. The cutting parameter-driven three-dimensional geometric modeling and simulation method for milling chips according to claim 1, characterized in that: In step S1, the specific method for obtaining the tool geometric parameters according to the tool model is: Step S11, constructing a milling cutter parameter database, wherein the primary key of the milling cutter parameter database is the cutter model, and the data segment is the cutter geometric parameters, including the number of cutter teeth, the cutter radius, and the cutting edge helix angle; Step S12: Obtain corresponding tool geometric parameters from the milling cutter parameter database according to the tool model.

3. The cutting parameter-driven milling chip three-dimensional geometric modeling and simulation method according to claim 1, characterized in that: In step S2, the method for obtaining the milling cutting parameters is: Get the NC code of the milling process; The NC code is parsed to obtain the tool feed speed and spindle speed of the current machining process, and the cutting width and cutting depth are determined based on the tool motion path information in the NC code.

4. The cutting parameter-driven milling chip three-dimensional geometric modeling and simulation method according to claim 1, characterized in that: In step S2, the method for obtaining the milling cutting parameters is: According to the real-time detection information of the machine tool's encoding sensor and preset supplementary parameters, the real-time position of the milling machine, spindle speed, tool feed information, cutting width, and cutting depth are determined. The tool feed information includes tool position and tool feed speed.

5. The cutting parameter-driven three-dimensional geometric modeling and simulation method for milling chips according to claim 4, characterized in that: In step S4, three-dimensional geometric modeling and simulation of the chip shape are performed to achieve two functions, namely, pre-processing simulation function and real-time monitoring function during processing: The pre-processing simulation function is to display the predicted milling chip shape in three dimensions according to the geometric parameters of the milling chip when it breaks; The real-time monitoring function during machining refers to the dynamic three-dimensional display of the milling chip profile based on the real-time tool feed information obtained from the encoder coding information.

6. The cutting parameter driven milling chip three-dimensional geometric modeling and simulation method according to claim 5, characterized in that: In the process of three-dimensional geometric modeling and simulation of the chip shape, the preset three-dimensional display accuracy requirements are achieved by adjusting the helix angle increment of the chip drawing and then changing the number of discrete triangular facets.

7. A cutting parameter driven milling chip three-dimensional geometric modeling and simulation system, characterized in that: include: Tool geometry parameter extraction module, used to obtain tool geometry parameters based on tool model; Cutting parameter extraction module, used to obtain milling cutting parameters; The chip shape geometric parameter calculation module is used to determine the shape geometric parameters of the milling chip when it breaks based on the tool geometric parameters and the milling cutting parameters, specifically including: Step S31, calculate the maximum thickness of the chip: if the cutting width a e Greater than the milling cutter radius R, the maximum chip thickness h max Equal to the feed per tooth f; if the cutting width a e Smaller than the milling cutter radius R, the maximum chip thickness h max for: Step S32, calculate the chip width: if the cutting width a e If it is greater than the milling cutter radius R, the chip width is the maximum chip width: L max =a p / sinα; Among them, a p represents the cutting depth, and α represents the cutting edge helix angle; Otherwise, the chip width L is calculated as: Step S33, calculating chip length: Wherein, Ls represents the chip length; Step S34, calculating the chip curling rate: the chip curling rate and the curling radius are inversely proportional, and the curling radius is: Where l represents the contact length of the chip, h represents the distance from the cutting plane of the tool face to the perpendicular line of the contact point between the chip and the tool, and w represents the distance from the tool tip to the cutting plane. The curling rate of the chip is Step S35, calculate the transverse curvature of the chip: the transverse curvature of the chip and the transverse curling radius are inversely proportional, and the transverse curling radius R cr The expression is: in, represents the lateral curvature of the chip; Step S36: Calculate the chip outflow angle: Where η represents the chip outflow angle, AB=a p / sinα, AC=f; The three-dimensional display module is used to perform three-dimensional geometric modeling and simulation of the chip shape when it breaks according to the geometric parameters of the chip shape when it breaks.

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