A method for optimizing the feed speed of spiral bevel gear milling

Abstract

This invention discloses a method for optimizing the feed rate in milling spiral bevel gears, comprising the following steps: Step 1, using a preset constant feed rate f const Step 1: Mill the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position; Step 2: Use the peak value of the tangential cutting force versus time curve as the allowable cutting force F of the tool. lim Alternatively, the allowable cutting force F of the tool can be obtained based on the equation. lim Then, the feed rate is adjusted and optimized based on the calculation formula, where i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th machining operation at a constant feed rate, and C represents the total number of tool position point numbers in the tool path. This can optimize the feed rate to improve milling efficiency and extend tool life.

Description

Technical Field

[0001] This invention relates to the field of spiral bevel gear milling technology, and more specifically to a method for optimizing the feed rate in spiral bevel gear milling. Background Technology

[0002] Spiral bevel gears, also known as spiral bevel gears, generally refer to bevel gears with curved pitch lines on their tooth surfaces. As a crucial basic component for transmitting motion between two intersecting or staggered shafts, they possess advantages such as a large overlap coefficient, smooth transmission, and high load-bearing capacity. They play a vital role in the manufacturing equipment industry and are widely used in precision machine tools, mining, aircraft, vehicles, ships, and energy sectors. The motion transmission of spiral bevel gears primarily relies on the conjugate tooth surfaces of a pair of meshing gears. The machining of these conjugate tooth surfaces involves complex cutting motions, typically achieved using multi-axis milling machines (usually requiring 3-5 axes) to control the relative generating or forming motions between the milling cutter and the gear blank. This complex milling principle leads to real-time changes in the shape of the undeformed chips during the milling process, making it difficult to predict cutting forces, select appropriate process parameters, and monitor the wear state of the milling cutter. In actual production, process parameters are usually selected based on empirical methods, resulting in the inability to fully utilize the cutting performance of existing milling cutters; the wear state of the milling cutter is usually judged by human observation, but the results of this method vary from person to person. Existing research mainly focuses on end milling and cylindrical gear machining, and often employs finite element analysis to obtain cutting forces during the machining process, which increases the analysis time cost. Meanwhile, milling process parameters and cutter wear conditions are the main factors affecting milling efficiency, cost, and tooth surface quality. Therefore, optimizing milling process parameters and monitoring cutter wear are essential to improving milling efficiency, ensuring machining quality, and reducing production costs.

[0003] Milling process parameters are the main factors affecting milling efficiency, tooth surface quality, and milling cutter wear. Increasing the feed rate increases the material removal rate per unit time, but it also leads to excessive cutting forces, accelerating tool wear and reducing tooth surface quality. Lower cutting parameters, to some extent, ensure tooth surface quality and reduce cutter head wear, but prolong machining time, reduce machining efficiency, and increase production costs. Therefore, selecting reasonable milling process parameters can not only improve machining efficiency and ensure tooth surface quality, but also help reduce milling cutter wear and extend cutter life. Currently, the selection of milling process parameters usually relies on existing literature and relevant experience. This method has limitations (the parameters are often conservatively selected and cannot fully utilize the cutting performance of the milling cutter), reducing milling cutting efficiency. Furthermore, according to the bevel gear machining principle, the cutting area changes in real time during the cutting process. To ensure that the difference in cutting area is not large each time and the cutting force is relatively stable, machining parameters such as feed rate should be adjusted accordingly. For traditional mechanical milling machines, the purely mechanical structure restricts this method of optimizing process parameters during the cutting process. However, with the development of CNC technology, fully CNC spiral bevel gear milling machines (which eliminate traditional complex mechanisms such as rocking tables, tool tilting, and deformation, and establish six-axis linkage) have been widely used in bevel gear machining, providing feasibility for flexibly controlling parameters during the cutting process. Currently, research on optimizing cutting parameters mainly uses finite element analysis to obtain cutting forces during the cutting process to optimize the feed rate. However, this method has high analysis time costs, and research is mostly concentrated on milling and cylindrical gear machining processes. Therefore, in order to improve milling efficiency and ensure milling quality, research on optimizing milling process parameters is necessary. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the feed rate in milling spiral bevel gears, which can optimize the feed rate, improve milling efficiency, reduce tool wear, and extend tool life.

[0005] The method for optimizing the feed rate in milling spiral bevel gears according to the present invention includes the following steps:

[0006] Step 1: Use a preset constant feed rate f const Milling is performed on the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position;

[0007] Step 2: The peak value in the curve of tangential cutting force versus time is taken as the allowable cutting force F of the tool. lim Based on computation The feed rate is adjusted and optimized, where i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c(i) represents the tangential cutting force at the tool position point during the i-th machining operation at a constant feed rate, and C represents the total number of tool position point numbers in the tool path.

[0008] Furthermore, in step two, F c The formula for (i) is:

[0009] θ c1 =cos(φ i )·cos(φ n )·cos(λ s ), θ c2 =sin(φ) n )·sin(λ s ), θ c3 =sin(φ) n )·cos(λ s )·cos(φ i )·tan(φ n +θ n );

[0010] In the formula, S A τ represents the cutting area of ​​the milling cutter during the i-th machining operation. s λ is the shear stress of the gear blank. s The cutting edge inclination angle, φ, is the angle between the cutting edge and the cutting speed. i φ is the shear flow angle. n θ is the normal shear angle. n Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

[0011] Furthermore, the calculation of the cutting area S(i) of the milling cutter includes the following steps:

[0012] 1) Based on the preset milling parameters, calculate the milling cutter position r for the i-th machining operation. c (i) refers to the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the gear cone to be machined as the origin of the milling machine, and the position of the milling cutter r is obtained. c (i) The corresponding gear blank position vector r g ;

[0013] 2) Based on the preset gear blank parameters and milling cutter parameters, the OpenCASCADE geometry engine is used to construct the gear blank solid model A(0) and the milling cutter solid model B(0) respectively;

[0014] 3) Adjust the gear blank solid model and the milling cutter solid model to the i-th machining position. The position of the gear blank solid model is represented as:

[0015] A(position i) = A(i-1)·RRot (n g ,dA), A(i-1) is the solid model of the gear blank after the (i-1)th machining, R Rot (n g ,dA) represents the solid model of the gear blank after the (i-1)th machining process, around n g Axis rotation dA, n g Let dA be the central axis of the gear blank solid model after the (i-1)th machining, and dA be the position A(i) of the gear blank solid model during the i-th machining. 位置 ) relative to the position A(i-1) of the gear blank solid model during the (i-1)th machining operation 位 Place) around axis n g The angle of rotation is the increment of the angle of the solid model of the gear blank around the A-axis between two different machining positions;

[0016] The position of the milling cutter solid model is represented as: B(i 位置 )=B(0)·T Trans (r c (i)), T Trans (r c (i) represents the milling cutter solid model B(0) in the machine tool coordinate system, which moves from the origin along the vector r. c (i) Move;

[0017] A(i 位置 ) and B(i 位置 Perform a Boolean intersection operation to obtain the material-removed entity R(i) for the i-th processing step;

[0018] 4) In the tool turret coordinate system during the i-th machining operation, according to the preset angle By repeatedly rotating the inner and outer cutter head sections at equal angles, a set H of inner cutter head sections arranged at equal angles around the cutter head axis is obtained. in and the set of external tool cross-section entities H out The inner tool section entity H, rotated j-th time, is part of the inner and outer tool section entity sets. in (i,j) and the external cutting cross-section entity H out (i,j) are subjected to Boolean intersection operations with the material removal entity R(i) in the i-th machining process to obtain the material removal entities of the inner and outer tools during the j-th rotation in the i-th machining process. The area extraction function module in the OpenCASCADE geometry engine is used to obtain the cutting area S of the inner tool during the j-th rotation in the i-th machining process. in (i,j) and the cutting area S of the external tool out (i,j),

[0019]

[0020] 5) By comparing the inner cutting angle, inner cutting angle, outer cutting angle, and outer cutting angle of the i-th machining process with θ p Based on the relationship, it can be determined whether the i-th machining operation is a single-tool cutting or multi-tool cutting, and the cutting area S of the milling cutter during the i-th machining operation can be calculated according to the cutting method. A ; In the formula N p This represents the total number of internal and external cutting teeth on the milling cutter head.

[0021] Furthermore, the determination of whether to perform single-blade cutting or multi-blade cutting in step 5) specifically involves:

[0022] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining operation is determined to be a single-blade cutting operation;

[0023] At this point, the cutting area S of the milling cutter during the i-th machining operation A for:

[0024]

[0025] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then it is determined that the i-th machining is a multi-blade cutting, and the outer blade has not completely cut out when the inner blade enters;

[0026] The angle θ between the inner and outer blades jk for:

[0027] The overlapping cutting areas are S in,out :

[0028]

[0029] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0030]

[0031] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ pThe relationship is Then it is determined that the i-th processing is multi-blade cutting, and the inner blade has not completely cut out when the outer blade enters;

[0032] At this moment, the angle θ between the inner and outer blades coincides. jk for:

[0033] The overlapping cutting areas are S in,out :

[0034]

[0035] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0036]

[0037] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining is determined to be multi-tool cutting, and the inner and outer tools have overlapping areas when cutting in and out, that is, they have two overlapping cutting angles.

[0038] At this moment, the angle θ between the inner and outer blades coincides. jk θ jk_2 for:

[0039]

[0040] The overlapping cutting areas are S in,out :

[0041]

[0042] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0043]

[0044] Furthermore, the shear stress τ s The formula for calculation is:

[0045] In the formula, A, B, C, n, and m are all material constants, determined according to the material properties of the gear blank, and γ is the shear strain. Shear strain rate The reference shear strain rate is T, where T is the absolute temperature. r For reference temperature, T m It is the melting temperature;

[0046] The φ i φ n θ n The calculation is as follows: Establish a coordinate system Σ:xyz, where the y-axis coincides with the cutting edge CD, the x-axis is perpendicular to the cutting edge, the z-axis is determined by the right-hand rule, the xoz plane is defined as the normal plane, the xoy plane is defined as the cutting plane, and the plane in which the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane.

[0047] The φ n The calculation formula is

[0048] The φ i The calculation formula is

[0049] The θ n The formula for calculating θ is n =β n -γ n ,

[0050] In the formula β n The average normal friction angle between the tool's rake face and the cutting plane. In the formula, f0 and p are constants, and v c For chip velocity, η λ γ is the debris angle. n The angle is forward.

[0051] A method for optimizing the feed rate in milling spiral bevel gears, characterized by comprising the following steps:

[0052] Step 1: Use a preset constant feed rate f const Milling is performed on the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position;

[0053] Step 2, based on the equation Calculate the allowable cutting force F of the tool lim ,

[0054] In the formula, i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th milling operation at a constant feed rate, C is the total number of tool position point indices in the tool path, and d const This is the distance between the tool positions during two adjacent machining operations;

[0055] Step 3, based on the calculation formula Adjusting and optimizing the feed rate reduces the tangential cutting force at the tool position during gear milling, lowers the cutting temperature, reduces tool wear, and extends tool life.

[0056] Furthermore, in step two, F c The formula for (i) is:

[0057] θ c1 =cos(φ i )·cos(φ n )·cos(λ s ), θ c2 =sin(φ) n )·sin(λ s ), θ c3 =sin(φ) n )·cos(λ s )·cos(φ i )·tan(φ n +θ n );

[0058] In the formula, S A τ represents the cutting area of ​​the milling cutter during the i-th machining operation. s λ is the shear stress of the gear blank. s The cutting edge inclination angle, φ, is the angle between the cutting edge and the cutting speed. i φ is the shear flow angle. n θ is the normal shear angle. n Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

[0059] Furthermore, the calculation of the cutting area S(i) of the milling cutter includes the following steps:

[0060] 1) Based on the preset milling parameters, calculate the milling cutter position r for the i-th machining operation. c (i) refers to the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the gear cone to be machined as the origin of the milling machine, and the position of the milling cutter r is obtained. c (i) The corresponding gear blank position vector r g ;

[0061] 2) Based on the preset gear blank parameters and milling cutter parameters, the OpenCASCADE geometry engine is used to construct the gear blank solid model A(0) and the milling cutter solid model B(0) respectively;

[0062] 3) Adjust the gear blank solid model and the milling cutter solid model to the i-th machining position. The position of the gear blank solid model is represented as:

[0063] A(i 位置)=A(i-1)·R Rot (n g ,dA), A(i-1) is the solid model of the gear blank after the (i-1)th machining, R Rot (n g ,dA) represents the solid model of the gear blank after the (i-1)th machining process, around n g Axis rotation dA, n g Let dA be the central axis of the gear blank solid model after the (i-1)th machining, and dA be the position A(i) of the gear blank solid model during the i-th machining relative to the position A(i-1) of the gear blank solid model during the (i-1)th machining. 位置 ) about axis n g The angle of rotation is the increment of the angle of the solid model of the gear blank around the A-axis between two different machining positions;

[0064] The position of the milling cutter solid model is represented as: B(i position) = B(0)·T Trans (r c (i)), T Trans (r c (i) represents the milling cutter solid model B(0) in the machine tool coordinate system, which moves from the origin along the vector r. c (i) Move;

[0065] Perform a Boolean intersection operation on A(i position) and B(i position) to obtain the material removal entity R(i) for the i-th processing step;

[0066] 4) In the tool turret coordinate system during the i-th machining operation, according to the preset angle By repeatedly rotating the inner and outer cutter head sections at equal angles, a set H of inner cutter head sections arranged at equal angles around the cutter head axis is obtained. in and the set of external tool cross-section entities H out The inner tool section entity H, rotated j-th time, is part of the inner and outer tool section entity sets. in (i,j) and the external cutting cross-section entity H out (i,j) are subjected to Boolean intersection operations with the material removal entity R(i) in the i-th machining process to obtain the material removal entities of the inner and outer tools during the j-th rotation in the i-th machining process. The area extraction function module in the OpenCASCADE geometry engine is used to obtain the cutting area S of the inner tool during the j-th rotation in the i-th machining process. in (i,j) and the cutting area S of the external tool out (i,j),

[0067]

[0068] 5) By comparing the inner cutting angle, inner cutting angle, outer cutting angle, and outer cutting angle of the i-th machining process with θ pBased on the relationship, it can be determined whether the i-th machining operation is a single-tool cutting or multi-tool cutting, and the cutting area S of the milling cutter during the i-th machining operation can be calculated according to the cutting method. A ; In the formula N p This represents the total number of internal and external cutting teeth on the milling cutter head.

[0069] Furthermore, the determination of whether to perform single-blade cutting or multi-blade cutting in step 5) specifically involves:

[0070] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining operation is determined to be a single-blade cutting operation;

[0071] At this point, the cutting area S of the milling cutter during the i-th machining operation A for:

[0072]

[0073] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then it is determined that the i-th machining is a multi-blade cutting, and the outer blade has not completely cut out when the inner blade enters;

[0074] The angle θ between the inner and outer blades jk for:

[0075] The overlapping cutting areas are S in,out :

[0076]

[0077] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0078]

[0079] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then it is determined that the i-th processing is multi-blade cutting, and the inner blade has not completely cut out when the outer blade enters;

[0080] At this moment, the angle θ between the inner and outer blades coincides. jk for:

[0081] The overlapping cutting areas are S in,out :

[0082]

[0083] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0084]

[0085] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining is determined to be multi-tool cutting, and the inner and outer tools have overlapping areas when cutting in and out, that is, they have two overlapping cutting angles.

[0086] At this moment, the angle θ between the inner and outer blades coincides. jk θ jk_2 for:

[0087]

[0088] The overlapping cutting areas are S in,out :

[0089]

[0090] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0091]

[0092] Furthermore, the shear stress τ s The formula for calculation is: In the formula, A, B, C, n, and m are all material constants, determined according to the material properties of the gear blank, and γ is the shear strain. Shear strain rate The reference shear strain rate is T, where T is the absolute temperature. r For reference temperature, T m It is the melting temperature;

[0093] The φ i φ n θ nThe calculation is as follows: Establish a coordinate system Σ:xyz, where the y-axis coincides with the cutting edge CD, the x-axis is perpendicular to the cutting edge, the z-axis is determined by the right-hand rule, the xoz plane is defined as the normal plane, the xoy plane is defined as the cutting plane, and the plane in which the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane.

[0094] The φ n The calculation formula is

[0095] The φ i The calculation formula is

[0096] The θ n The formula for calculating θ is n =β n -γ n ,

[0097] In the formula β n The average normal friction angle between the tool's rake face and the cutting plane. In the formula, f0 and p are constants, and v c For chip velocity, η λ γ is the debris angle. n The angle is forward.

[0098] Compared with the prior art, the present invention has the following beneficial effects.

[0099] 1. The present invention first performs milling at a preset constant feed rate to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position. Then, based on the obtained relationship curve between tangential cutting force and time, the allowable cutting force of the tool is calculated. The feed rate is adjusted using a specific calculation formula to complete the feed rate optimization, thereby improving feed efficiency or extending tool life.

[0100] 2. This invention uses the peak value in the curve of tangential cutting force versus time as the allowable cutting force of the tool, and uses a specific calculation formula to adjust the feed rate so that the cutting force of each cut approaches the allowable cutting force of the tool. This increases the feed rate in stages with smaller cutting areas, shortens the overall milling process time, and improves cutting efficiency.

[0101] 3. This invention establishes an equation under the condition that the cutting time before and after optimization is the same, calculates the allowable cutting force of the tool, and then adjusts the feed rate based on the allowable cutting force of the tool and a specific calculation formula, thereby reducing the tangential cutting force at the tool position during the milling process, reducing the cutting temperature, reducing tool wear, and extending the tool life. Attached Figure Description

[0102] Figure 1This is a schematic diagram of the relationship between tangential cutting force and time when milling gears at a constant feed rate from a basic rocking table angle.

[0103] Figure 2 This is a schematic diagram of the relationship between tangential cutting force and time when milling gears from the basic rocking table angle at the optimized feed rate in Example 1.

[0104] Figure 3 This is a schematic diagram of the feed rate variation of the milling gear optimized by the basic rocking table angle feed rate in Example 1;

[0105] Figure 4 A schematic diagram showing the relationship between tangential cutting force and time when milling gears at a constant feed rate with an initial rocking table angle in Example 1;

[0106] Figure 5 This is a schematic diagram of the relationship between tangential cutting force and time when milling gears at an optimized feed rate from the initial rocking table angle in Example 1.

[0107] Figure 6 This is a schematic diagram showing the change in feed rate of the milling gear after optimizing the feed rate of the starting table angle;

[0108] Figure 7 This is a schematic diagram of the relationship between tangential cutting force and time when milling gears from the basic rocking table angle at the optimized feed rate in Example 2.

[0109] Figure 8 This is a schematic diagram of the feed rate variation of the milling gear with the basic rocking table angle feed rate optimization in Example 2;

[0110] Figure 9 This is a schematic diagram of the relationship between tangential cutting force and time when milling gears at the optimized feed rate from the initial rocking table angle in Example 2.

[0111] Figure 10 This is a schematic diagram of the feed rate change of the milling gear when the initial rocking table angle feed rate is optimized in Example 2;

[0112] Figure 11 This is a schematic diagram of the optimized feed rate change in the milling cutter life verification test in Example 2. Detailed Implementation

[0113] The present invention will now be described in detail with reference to the accompanying drawings.

[0114] Example 1: A method for optimizing the feed rate in milling spiral bevel gears, comprising the following steps:

[0115] Step 1: Use a preset constant feed rate f constMilling is performed on the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position;

[0116] Step 2: The peak value in the curve of tangential cutting force versus time is taken as the allowable cutting force F of the tool. lim Based on computation The feed rate is adjusted and optimized, where i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th machining operation at a constant feed rate, and C is the tool position point number in the tool path.

[0117] In step two, F c The formula for (i) is:

[0118] θ c1 =cos(φ i )·cos(φ n )·cos(λ s ), θ c2 =sin(φ) n )·sin(λ s ), θ c3 =sin(φ) n )·cos(λ s )·cos(φ i )·tan(φ n +θ n );

[0119] In the formula, S A τ represents the cutting area of ​​the milling cutter during the i-th machining operation. s λ is the shear stress of the gear blank. s The cutting edge inclination angle, φ, is the angle between the cutting edge and the cutting speed. i φ is the shear flow angle. n θ is the normal shear angle. n Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

[0120] The calculation of the cutting area S(i) of the milling cutter includes the following steps:

[0121] 1) Based on the preset milling parameters, calculate the milling cutter position r for the i-th machining operation. c (i) refers to the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the gear cone to be machined as the origin of the milling machine, and the position of the milling cutter r is obtained. c (i) The corresponding gear blank position vector r g ;

[0122] 2) Based on the preset gear blank parameters and milling cutter parameters, the OpenCASCADE geometry engine is used to construct the gear blank solid model A(0) and the milling cutter solid model B(0) respectively;

[0123] 3) Adjust the gear blank solid model and the milling cutter solid model to the i-th machining position. The position of the gear blank solid model is represented as:

[0124] A(i 位置 )=A(i-1)·R Rot (n g ,dA), A(i-1) is the solid model of the gear blank after the (i-1)th machining, R Rot (n g ,dA) represents the solid model of the gear blank after the (i-1)th machining process, around n g Axis rotation dA, n g Let dA be the central axis of the gear blank solid model after the (i-1)th machining, and dA be the position A(i) of the gear blank solid model during the i-th machining. 位置 ) relative to the position A(i-1) of the gear blank solid model during the (i-1)th machining operation 位置 ) about axis n g The angle of rotation is the increment of the angle of the solid model of the gear blank around the A-axis between two different machining positions;

[0125] The position of the milling cutter solid model is represented as: B(i 位置 )=B(0)·T Trans (r c (i)), T Trans (r c (i) represents the milling cutter solid model B(0) in the machine tool coordinate system, which moves from the origin along the vector r. c (i) Move;

[0126] A(i 位置 ) and B(i 位置 Perform a Boolean intersection operation to obtain the material-removed entity R(i) for the i-th processing step;

[0127] 4) In the tool turret coordinate system during the i-th machining operation, according to the preset angle By repeatedly rotating the inner and outer cutter head sections at equal angles, a set H of inner cutter head sections arranged at equal angles around the cutter head axis is obtained. in and the set of external tool cross-section entities H out The inner tool section entity H, rotated j-th time, is part of the inner and outer tool section entity sets. in (i,j) and the external cutting cross-section entity H out(i,j) are subjected to Boolean intersection operations with the material removal entity R(i) in the i-th machining process to obtain the material removal entities of the inner and outer tools during the j-th rotation in the i-th machining process. The area extraction function module in the OpenCASCADE geometry engine is used to obtain the cutting area S of the inner tool during the j-th rotation in the i-th machining process. in (i,j) and the cutting area S of the external tool out (i,j),

[0128]

[0129] 5) By comparing the inner cutting angle, inner cutting angle, outer cutting angle, and outer cutting angle of the i-th machining process with θ p Based on the relationship, it can be determined whether the i-th machining operation is a single-tool cutting or multi-tool cutting, and the cutting area S of the milling cutter during the i-th machining operation can be calculated according to the cutting method. A ; In the formula N p This represents the total number of internal and external cutting teeth on the milling cutter head.

[0130] The determination of whether it is single-blade cutting or multi-blade cutting is specifically as follows:

[0131] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining operation is determined to be a single-blade cutting operation;

[0132] At this point, the cutting area S of the milling cutter during the i-th machining operation A for:

[0133]

[0134] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then it is determined that the i-th machining is a multi-blade cutting, and the outer blade has not completely cut out when the inner blade enters;

[0135] The angle θ between the inner and outer blades jk for:

[0136] The overlapping cutting areas are S in,out :

[0137]

[0138] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0139]

[0140] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then it is determined that the i-th processing is multi-blade cutting, and the inner blade has not completely cut out when the outer blade enters;

[0141] At this moment, the angle θ between the inner and outer blades coincides. jk for:

[0142] The overlapping cutting areas are S in,out :

[0143]

[0144] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0145]

[0146] If the internal cutting angle of the i-th machining... Inner blade cutting angle external blade cutting angle external blade cutting angle With θ p The relationship is Then the i-th machining is determined to be multi-tool cutting, and the inner and outer tools have overlapping areas when cutting in and out, that is, they have two overlapping cutting angles.

[0147] At this moment, the angle θ between the inner and outer blades coincides. jk θ jk_2 for:

[0148]

[0149] The overlapping cutting areas are S in,out :

[0150]

[0151] Then, the cutting area S of the milling cutter during the i-th machining operation A for:

[0152]

[0153] The shear stress τ s The formula for calculation is: In the formula, A, B, C, n, and m are all material constants, determined according to the material properties of the gear blank, and γ is the shear strain. Shear strain rate The reference shear strain rate is T, where T is the absolute temperature. r For reference temperature, T m This is the melting temperature.

[0154] In this embodiment, the blank material is 20CrMnTi, and the values ​​of various constants and thermophysical properties are shown in Table 1.

[0155] Table 1 Material constants for the JC constitutive model of 20CrMnTi

[0156]

[0157] The φ i φ n θ n The calculation is as follows: Establish a coordinate system Σ:xyz, where the y-axis coincides with the cutting edge CD, the x-axis is perpendicular to the cutting edge, the z-axis is determined by the right-hand rule, the xoz plane is defined as the normal plane, the xoy plane is defined as the cutting plane, and the plane in which the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane.

[0158] The φ n The calculation formula is

[0159] The φ i The calculation formula is

[0160] The θ n The formula for calculating θ is n =β n -γ n ,

[0161] In the formula β n The average normal friction angle between the tool's rake face and the cutting plane. In the formula, f0 and p are constants, and v c For chip velocity, η λ γ is the debris angle. n The angle is forward.

[0162] The method for optimizing the feed speed of spiral bevel gears described in this invention was verified through specific milling cutting examples. The actual milling experiment was completed using a YKH2235 CNC spiral bevel gear milling machine manufactured by Tianjin No.1 Machine Tool Plant. The parameters of the spiral bevel gear blank, the milling machine adjustment parameters, and the gear roughing cutter parameters in the actual milling experiment are shown in Tables 2 to 4, respectively.

[0163] Table 2 Parameters of Spiral Bevel Gear Blank

[0164] Parameters / Units numerical values Parameters / Units numerical values Number of teeth 11 Cone angle / ° 23.9 Modulus 4.024 Cone angle / ° 19.7 Tooth width / mm 27.64 Distance between the vertex of the cone and the point where the shaft intersects (mm) 1.4 Rotation Left-handed Distance between the vertex of the root cone and the point where the axis intersects (mm) -1.22 Helix angle / ° 49.8 Distance between the vertex of the cone and the point where they intersect the axis / mm 0.38 Theoretical total tooth height / mm 8.02 Distance from the crown to the axle intersection point / mm 79.25 Root cone angle / ° 18.9 Distance from front wheel crown to axle intersection point / mm 53.98

[0165] Table 3 Adjustment parameters for gear milling machine

[0166] Parameters / Units numerical values Parameters / Units numerical values Horizontal wheel position / mm 1.78 Machine tool mounting root cone angle / ° 18.9 bed / mm -0.97 Starting rocking table angle / ° 48.51012 Vertical wheel position / mm 23.86 Termination of rocking table angle / ° 86.04795 Radial tool position / mm 69.86 Basic rocking table angle / ° 67.61651 Rolling ratio 4.09179

[0167] Table 4. Gear rough milling cutter parameters

[0168] Parameters / Units numerical values nominal diameter of cutter head / mm 127 External cutting tool tooth profile angle / ° 14 Internal cutting tool tooth profile angle / ° 24 Internal and external cutting edge misalignment / mm 2.54 Cutter tip radius / mm 0.99

[0169] The milling cutter is a roughing cutter head from Harbin Tool Factory, with eight internal and eight external inserts, for a total of sixteen inserts. The insert material is high-speed steel, with a rake angle of 20° and a cutting edge inclination angle of 5°. The gear blank material is 20CrMnTi, and oil bath cooling is used for cutting.

[0170] The rotor of the rotary force gauge is connected to the milling machine spindle at one end via a spindle adapter, and to the cutter head at the other end via a customized cutter head adapter. The stator is fixed to the spindle end face via a self-made simple bracket and connected to a signal acquisition unit using a high-insulation impedance cable for signal transmission. The force gauge parameters are set and cutting force analysis is displayed during the cutting process using DynoWare software on a laptop. To expand the application scope of the cutting force calculation model and considering the limitations of the machine tool's mechanical structure, experiments were conducted under two different milling cutting conditions:

[0171] The first condition is that the cutter head cuts into the theoretical full tooth height from the basic rocking table angle position. At this time, the tooth blank is fixed and there is no rolling motion between the cutter head and the tooth blank. The cutting situation between the two is similar to the form milling method.

[0172] The second condition is that the cutter head starts cutting from the initial rocking table angle and develops from the large end to the small end. At this time, there is a rolling motion between the cutter head and the blank.

[0173] First, helical gear milling was performed under both conditions at a constant feed rate of 30 mm / min. The relationship curves between tangential cutting force and time during the milling process at the tool position were obtained, as shown in the respective figures. Figure 1 and Figure 4 .

[0174] Then, the peak value in the curve of tangential cutting force versus time is taken as the allowable cutting force F of the tool. lim Based on computation The feed rate is adjusted and optimized, where i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th milling operation at a constant feed rate, where C is the tool position point number in the tool path. The optimized feed rates under the two experimental conditions are described in [reference 1]. Figure 3 and Figure 6 .

[0175] Finally, helical gear milling was performed under both the first and second conditions using the optimized feed rate. The relationship curves between tangential cutting force and time during the milling process at the tool position were obtained, as shown in the respective figures. Figure 2 and Figure 5 .

[0176] See Figure 1 Under the first condition, i.e., milling gears from the basic rocker table angle at a constant feed rate, the milling time is 11.6 s, and the peak tangential cutting force is approximately 1060 N. See also... Figure 2 Under the first condition, i.e., milling gears from the basic rocker table angle at the optimized feed rate, the milling time is 7.9 s, and the tangential cutting force fluctuates around 1045 N. (Based on Figure 1 and...) Figure 2 Comparative analysis shows that: with feed rate optimization, the tangential cutting force fluctuates around the allowable cutting force of the tool during gear milling, the cutting time is reduced by 3.7s, and the gear milling efficiency is improved by 31.9%.

[0177] See Figure 3 The optimized tangential cutting force refers to the tangential cutting force at the tool position when milling teeth at the optimized feed rate. The trend of the optimized feed rate is that it gradually decreases, which is the opposite of the trend of the tangential cutting force during constant feed rate cutting, which is that it gradually increases. This is consistent with actual cutting experience. The optimized tangential cutting force generally fluctuates around the desired tangential cutting force, but there is a large difference in the early stage of cutting. This is to reduce the impact generated by the cutter head when it first cuts into the tooth blank and to protect the cutter head from damage such as chipping. The feed rate in the early stage of milling is deliberately reduced.

[0178] See Figure 4 Under the second condition, i.e., milling at a constant feed rate from the initial rocker angle, the milling time is 42.6 s, and the peak tangential cutting force is approximately 1000 N. See also... Figure 5 Under the second condition, i.e., milling gears from the initial rocker table angle at the optimized feed rate, the milling time is 28.2s, and the tangential cutting force fluctuates around 930N. (Based on Figure 4 and...) Figure 5 Comparative analysis shows that: with feed rate optimization, the tangential cutting force fluctuates around the allowable cutting force of the tool in milling, the cutting time is reduced by 14.4s, and the milling efficiency is improved by 33.8%.

[0179] See Figure 6 The optimized feed rate first decreases, then increases slowly, and finally increases rapidly. This trend is opposite to the trend of tangential cutting force during constant cutting speed cutting, which is consistent with actual cutting experience. Similarly, to avoid a large impact on the cutter head during the initial entry, the feed rate in the early stage of cutting is reduced, resulting in a certain difference between the experimentally measured early tangential cutting force and the expected tangential cutting force. However, the tangential cutting force fluctuates around the set expected tangential cutting force throughout the entire cutting process.

[0180] Example 2: A method for optimizing the feed rate in milling spiral bevel gears, comprising the following steps:

[0181] Step 1: Use a preset constant feed rate f const The gear blank is milled to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position.

[0182] Step 2, based on the equation Calculate the allowable cutting force F of the tool lim ,

[0183] In the formula, i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th milling operation at a constant feed rate, C is the total number of tool position point indices in the tool path, and d const This represents the distance between the tool positions during two adjacent machining operations.

[0184] Step 3, based on the calculation formula The feed rate was adjusted and optimized.

[0185] With a preset constant feed rate f const The milling cutting time for the gear blank is:

[0186] The milling time for the gear blank at the optimized feed rate f(i) is:

[0187] Based on T const =T vary and achievable Therefore, the allowable cutting force F of the tool can be obtained using this equation. limThen, based on the allowable cutting force of the tool and a specific calculation formula, the feed rate is adjusted. Under the condition that the cutting time before and after optimization is the same, the tangential cutting force at the tool position during the milling process is reduced, the cutting temperature is reduced, the tool wear is reduced, and the tool life is extended.

[0188] In step two, F c The formula for (i) is:

[0189] θ c1 =cos(φ i )·cos(φ n )·cos(λ s ), θ c2 =sin(φ) n )·sin(λ s ), θ c3 =sin(φ) n )·cos(λ s )·cos(φ i )·tan(φ n +θ n ).

[0190] In the formula, S A τ represents the cutting area of ​​the milling cutter during the i-th machining operation. s λ is the shear stress of the gear blank. s The cutting edge inclination angle, φ, is the angle between the cutting edge and the cutting speed. i φ is the shear flow angle. n θ is the normal shear angle. n Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

[0191] The cutting area S(i) and shear stress τ of the milling cutter during the i-th machining operation s and φ i φ n θ n The calculation is the same as in Example 1.

[0192] The method for optimizing the feed speed of spiral bevel gears described in this invention was verified through specific milling cutting examples. The actual milling experiment was completed using a YKH2235 CNC spiral bevel gear milling machine manufactured by Tianjin No.1 Machine Tool Plant. The parameters of the spiral bevel gear blank, the milling machine adjustment parameters, and the gear roughing cutter parameters in the actual milling experiment are shown in Tables 2 to 4, respectively.

[0193] The milling cutter is a roughing cutter head from Harbin Tool Factory, with eight internal and eight external inserts, for a total of sixteen inserts. The insert material is high-speed steel, with a rake angle of 20° and a cutting edge inclination angle of 5°. The gear blank material is 20CrMnTi, and oil bath cooling is used for cutting.

[0194] The rotor of the rotary force gauge is connected to the milling machine spindle at one end via a spindle adapter, and to the cutter head at the other end via a customized cutter head adapter. The stator is fixed to the spindle end face via a self-made simple bracket and connected to a signal acquisition unit using a high-insulation impedance cable for signal transmission. The force gauge parameters are set and cutting force analysis is displayed during the cutting process using DynoWare software on a laptop. To expand the application scope of the cutting force calculation model and considering the limitations of the machine tool's mechanical structure, experiments were conducted under two different milling cutting conditions:

[0195] The first condition is that the cutter head cuts into the theoretical full tooth height from the basic rocking table angle position. At this time, the tooth blank is fixed and there is no rolling motion between the cutter head and the tooth blank. The cutting situation between the two is similar to the form milling method.

[0196] The second condition is that the cutter head starts cutting from the initial rocking table angle and develops from the large end to the small end. At this time, there is a rolling motion between the cutter head and the blank.

[0197] First, helical gear milling was performed under both conditions at a constant feed rate of 30 mm / min. The relationship curves between tangential cutting force and time during the milling process at the tool position were obtained, as shown in the respective figures. Figure 1 and Figure 4 .

[0198] Then based on the equation Calculate the allowable cutting force F of the tool lim ,

[0199] In the formula, i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th milling operation at a constant feed rate, C is the total number of tool position point indices in the tool path, and d const This represents the distance between the tool positions during two adjacent machining operations.

[0200] Based on the calculation formula The feed rate was adjusted and optimized. See the optimized feed rates for the two test conditions respectively. Figure 7 and Figure 9 .

[0201] Finally, helical gear milling was performed under both the first and second conditions using the optimized feed rate. The relationship curves between tangential cutting force and time during the milling process at the tool position were obtained, as shown in the respective figures. Figure 8 and Figure 10 .

[0202] See Figure 1Under the first condition, i.e., milling gears from the basic rocker table angle at a constant feed rate, the milling time is 11.6 s, and the peak tangential cutting force is approximately 1060 N. See also... Figure 7 and Figure 8 Under the first condition, i.e., milling gears from the basic rocker table angle with the optimized feed rate, the machining time is 10.9s, and the peak tangential cutting force fluctuates around 910N. According to... Figure 1 and Figure 7 Comparative analysis shows that, under similar milling times, the tangential cutting force of the cutter head decreased by approximately 150 N, and the peak tangential cutting force decreased by 14.2%. Combined with the tool life model, the reduction in cutting force during gear milling leads to a decrease in cutting temperature, effectively mitigating cutter head wear and extending the life of the milling cutter.

[0203] See Figure 4 Under the second condition, i.e., milling at a constant feed rate from the initial rocker angle, the milling time is 42.6 s, and the peak tangential cutting force is approximately 1000 N. See also... Figure 9 and Figure 10 Under the second condition, i.e., milling gears from the initial rocker table angle at the optimized feed rate, the milling time is 43.7s, and the tangential cutting force fluctuates around 780N. According to... Figure 4 and Figure 9 Comparative analysis shows that, under similar milling times, the tangential cutting force of the cutter head decreased by approximately 220 N, and the peak tangential cutting force decreased by 22%. Combined with the tool life model, the reduction in cutting force during gear milling leads to a decrease in cutting temperature, effectively mitigating cutter head wear and extending the life of the milling cutter.

[0204] To study the monitoring of milling cutter wear during the milling process, a YKT2250 CNC spiral bevel gear milling machine manufactured by Tianjin No.1 Machine Tool Plant, a 3350-B-120 data acquisition module from Danish company B&K, a general-purpose three-axis CCLD accelerometer 4535-B, and PULSE LabShop data acquisition software were used to collect vibration signals during the milling process. Two three-axis accelerometers were respectively arranged at the first measurement position on the end face of the machine tool spindle and the second measurement position on the upper end face of the workpiece spindle.

[0205] For a newly sharpened cutter head, the number of workpieces processed is used as the wear state of the milling cutter, and vibration signals are measured and recorded every 5 products processed to form one milling cutter wear state. A total of 140 products were processed, and 28 processing wear states were recorded. Each time the vibration signal was measured, the vibration signals of the processing of 6 different tooth slots in a gear were measured as the original dataset. The vibration signals of any 5 tooth slots in the original dataset were used as the training set, and the vibration signal of the processing of the remaining tooth slot was used as the test set.

[0206] Feature values ​​were extracted from the monitored milling vibration signals, including 5 statistical feature values ​​in the time domain, 3 feature values ​​in the frequency domain, 32 feature values ​​in the wavelet packet, and feature values ​​for the cutting frequency amplitude and harmonic amplitude, totaling 50 feature values. Since these monitoring signals are from three directions at two monitoring locations, the original number of feature values ​​is 300. These feature values ​​were then encoded accordingly, as shown in Table 5.

[0207] Table 5 Feature value encoding of monitored vibration signals

[0208]

[0209] Constructing a prediction model for the wear state of milling cutters includes the following steps:

[0210] (1) Import the collected raw data, with 140 sample data as training set data and 28 sample data as test set data;

[0211] (2) Normalize the training set data and test set data and use them as input data for the support vector machine regression model, with the number of processed products as the output;

[0212] (3) V-fold cross-validation was used to select the optimal parameter values ​​of c and g in the support vector machine. The results showed that c was 86.9501 and g was 0.01.

[0213] (4) The ReliefF Algorithm is used to sort the feature weights and select a reasonable number of feature values;

[0214] (5) Train the support vector machine regression model using the training set data;

[0215] (6) Input the test set data and use the trained regression model to predict the wear state of the milling cutter, so as to obtain a milling cutter wear state prediction model that meets the requirements.

[0216] To further verify the feasibility and effectiveness of the milling cutter life feed rate optimization method, the feed rate of a gear milling product was optimized using the method described in this invention. The wear state of the milling cutter during the milling process was monitored using a milling cutter wear monitoring experiment device, and the milling cutter life was predicted using a constructed milling cutter wear state prediction model. The gear blank parameters, machine tool adjustment parameters, and milling cutter parameters of the gear product to be processed are shown in Tables 6, 7, and 8, respectively.

[0217] Table 6 Parameters of Spiral Bevel Gear Blank

[0218] Parameters / Units numerical values Parameters / Units numerical values Number of teeth 31 Cone angle / ° 76.01 Modulus 4.5 Cone angle / ° 72.01 Tooth width / mm 18 Distance from the apex of the cone to the wheel crown / mm 20.38 Rotation right-handed Distance between the vertex of the root cone and the point where the axis intersects (mm) 2.09 Helix angle / ° 25 Distance between the vertex of the cone and the point where they intersect the axis / mm -2.85 Theoretical total tooth height / mm 8.93 Distance from front wheel crown to the top of the pitch cone / mm 16.03 Root cone angle / ° 65.4

[0219] Table 7 Machine Tool Adjustment Parameters

[0220] Parameters / Units numerical values Parameters / Units numerical values Horizontal wheel position / mm 0 Machine tool mounting root cone angle / ° 65.4 bed / mm 1.7 Starting rocking table angle / ° 45 Vertical wheel position / mm 0 Termination of rocking table angle / ° 80 Radial tool position / mm 76.15 Basic rocking table angle / ° 65.08 Rolling ratio 1.05

[0221] Table 8. Milling cutter parameters

[0222] Parameters / Units numerical values nominal diameter of cutter head / mm 152.4 External cutting tool tooth profile angle / ° 17.7 Internal cutting tool tooth profile angle / ° 22.2 Internal and external cutting edge misalignment / mm 3.05 Cutter tip radius / mm 1.06

[0223] By analyzing the kinematic relationship of spiral bevel gear milling, the theory of metal oblique cutting and the material constitutive equation were introduced. Based on the milling cutter structure and milling motion, a mathematical model of milling cutting force was established, accurately predicting the milling cutting force of spiral bevel gears. The results are shown in [reference needed]. Figure 11 In the figure, the dashed triangle represents the predicted tangential cutting force of the milling gear, the solid square represents the optimized feed rate, and the solid circle represents the desired tangential cutting force. The predicted tangential cutting force rises rapidly in the early stage, reaches its peak, and then tends to decrease at a constant rate, which is basically consistent with the milling process observed on site.

[0224] Milling was performed using an optimized feed rate. Vibration signals from 95–120 milled products were collected using a milling cutter wear monitoring device, with data collected every 5 products as one state. The constructed milling cutter wear state prediction model was used to predict the milling cutter life during milling with optimized feed rate. The predicted values ​​are shown in Table 9.

[0225] Table 9. Predicted wear values ​​of milling cutters after feed rate optimization

[0226] Sample number Predicted value Predicted number of parts to be processed Actual number of processed pieces 1 75.76 75 95 2 82.25 80 100 3 81.91 80 105 4 91.01 90 110 5 95.41 95 115 6 95.48 95 120

[0227] It is evident that the predicted number of milled parts after feed rate optimization is lower than the actual number of milled parts. Considering that the prediction error of the prediction model within a certain category range will not exceed 5 parts, this indicates that the milling cutter with optimized feed rate can process 10 to 20 more products, verifying the feasibility and effectiveness of the feed rate optimization method based on milling cutter lifespan.

Claims

1. A method for optimizing the feed rate in milling spiral bevel gears, characterized in that, Includes the following steps: Step 1: Use a preset constant feed rate f const Milling is performed on the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position; Step 2: The peak value in the curve of tangential cutting force versus time is taken as the allowable cutting force F of the tool. lim Based on computation By adjusting and optimizing the feed rate, the cutting force of each cut is made close to the allowable cutting force of the tool, thereby increasing the feed rate in stages with smaller cutting areas, shortening the overall milling process time, and improving cutting efficiency. In the formula, i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th machining operation at a constant feed rate, and C represents the total number of tool position point numbers in the tool path.

2. The method for optimizing the feed rate in milling spiral bevel gears according to claim 1, characterized in that, In step two, F c The formula for (i) is: , ， ， ； In the formula, S A Let be the cutting area of ​​the milling cutter during the i-th machining operation. The shear stress of the gear blank is... The cutting edge inclination angle is the angle between the cutting edge and the cutting speed. Shear flow angle, Normal shear angle, Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

3. The method for optimizing the feed rate in milling spiral bevel gears according to claim 2, characterized in that, The milling cutter has a cutting area S A The calculation includes the following steps: 1) Calculate the milling cutter position point for the i-th machining operation based on the preset milling parameters. That is, the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the gear cone to be machined as the origin of the milling machine, and the position relative to the milling cutter position. Corresponding tooth blank position vector ; 2) Based on the preset gear blank parameters and milling cutter parameters, the OpenCASCADE geometry engine is used to construct the gear blank solid model A(0) and the milling cutter solid model B(0) respectively; 3) Adjust the gear blank solid model and the milling cutter solid model to the i-th machining position. The position of the gear blank solid model is represented as: A(i 位置 ) = A(i-1)·R Rot (n g ,dA), A(i-1) is the solid model of the gear blank after the (i-1)th machining, R Rot (n g ,dA) represents the solid model of the gear blank after the (i-1)th machining process, around n g Axis rotation dA, n g Let dA be the central axis of the gear blank solid model after the (i-1)th machining, and dA be the position A(i) of the gear blank solid model during the i-th machining. 位置 ) relative to the position A(i-1) of the gear blank solid model during the (i-1)th machining operation 位置 ) about axis n g The angle of rotation is the increment of the angle of the solid model of the gear blank around the A-axis between two different machining positions; The position of the milling cutter solid model is represented as: B(i 位置 )=B(0)·T Trans (r c (i)), T Trans (r c (i) represents the solid model B(0) of the milling cutter in the machine tool coordinate system, which moves from the origin along the vector r. c (i) Move; A(i 位置 ) and B(i 位置 Perform a Boolean intersection operation to obtain the material-removed entity R(i) for the i-th processing step; 4) In the tool turret coordinate system during the i-th machining operation, according to the preset angle By repeatedly rotating the inner and outer cutter head sections at equal angles, a set H of inner cutter head sections arranged at equal angles around the cutter head axis is obtained. in and the set of external tool cross-section entities H out The inner tool section entity H, rotated j-th time, is part of the inner and outer tool section entity sets. in (i,j) and the external cutting cross-section entity H out (i,j) are subjected to Boolean intersection with the material removal entity R(i) in the i-th machining process to obtain the material removal entities of the inner and outer tools during the j-th rotation in the i-th machining process. The area extraction function module in the OpenCASCADE geometry engine is used to obtain the cutting area S of the inner tool during the j-th rotation in the i-th machining process. in (i,j) and the cutting area S of the external tool out (i,j), ； 5) By comparing the inner cutting angle, inner cutting angle, outer cutting angle, and outer cutting angle of the i-th machining process with... Based on the relationship, it can be determined whether the i-th machining operation is a single-tool cutting or multi-tool cutting, and the cutting area S of the milling cutter during the i-th machining operation can be calculated according to the cutting method. A ; In the formula N p This represents the total number of internal and external cutting teeth on the milling cutter head.

4. The method for optimizing the feed rate in milling spiral bevel gears according to claim 3, characterized in that, The determination of whether it is single-blade cutting or multi-blade cutting in step 5) is as follows: If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a single-blade cutting operation; At this point, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a multi-blade cutting operation, and the outer blade has not completely cut out when the inner blade enters the cutting operation; Angle of overlap between inner and outer blades for: ; The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a multi-blade cutting operation, and the inner blade has not yet completely cut out when the outer blade enters the cutting area; At this point, the angle of overlap between the inner and outer blades for: ; The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining is determined to be multi-blade cutting, and the inner and outer blades have overlapping areas when cutting in and out, that is, they have two overlapping cutting angles; At this point, the angle of overlap between the inner and outer blades , for: ； The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: 。 5. The method for optimizing the feed rate in milling spiral bevel gears according to claim 2, characterized in that, The shear stress The formula for calculation is: , In the formula, A, B, C, n, and m are all material constants, determined based on the material properties of the gear blank. For shear strain, Shear strain rate The reference shear strain rate is T, where T is the absolute temperature. r For reference temperature, T m It is the melting temperature; The , , The calculation specifically involves: establishing a coordinate system. The y-axis coincides with the cutting edge CD, the x-axis is perpendicular to the cutting edge, the z-axis is determined by the right-hand rule, the xoz plane is defined as the normal plane, the xoy plane is defined as the cutting plane, and the plane in which the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane. The The calculation formula is , The The calculation formula is , The The calculation formula is , In the formula The average normal friction angle between the tool's rake face and the cutting plane. In the formula , It is a constant. For chip speed, For the debris angle, The angle is forward.

6. A method for optimizing the feed rate in milling spiral bevel gears, characterized in that, Includes the following steps: Step 1: Use a preset constant feed rate f const Milling is performed on the gear blank to obtain the relationship curve between tangential cutting force and time during the milling process at the tool position; Step 2, based on the equation Calculate the allowable cutting force F of the tool lim , In the formula, i = 1, 2, 3, ..., C, f(i) is the optimized feed rate for the i-th machining operation, and F... c (i) represents the tangential cutting force at the tool position point during the i-th milling operation at a constant feed rate, C is the total number of tool position point indices in the tool path, and d const This is the distance between the tool positions during two adjacent machining operations; Step 3, based on the calculation formula Adjusting and optimizing the feed rate reduces the tangential cutting force at the tool position during gear milling, lowers the cutting temperature, reduces tool wear, and extends tool life.

7. The method for optimizing the feed rate in milling spiral bevel gears according to claim 6, characterized in that, In step two, F c The formula for (i) is: , ； In the formula, S A For the first The cutting area of ​​the milling cutter during the next machining operation. The shear stress of the gear blank is... The cutting edge inclination angle is the angle between the cutting edge and the cutting speed. Shear flow angle, Normal shear angle, Let x be the angle between the projection of the cutting force F onto the normal plane and the x-axis, where the x-axis is perpendicular to the cutting edge.

8. The method for optimizing the feed rate in milling spiral bevel gears according to claim 7, characterized in that, The milling cutter has a cutting area S A The calculation includes the following steps: 1) Calculate the milling cutter position point for the i-th machining operation based on the preset milling parameters. That is, the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the gear cone to be machined as the origin of the milling machine, and the position relative to the milling cutter position. Corresponding tooth blank position vector ; 2) Based on the preset gear blank parameters and milling cutter parameters, the OpenCASCADE geometry engine is used to construct the gear blank solid model A(0) and the milling cutter solid model B(0) respectively; 3) Adjust the gear blank solid model and the milling cutter solid model to the i-th machining position. The position of the gear blank solid model is represented as: A(i 位置 ) = A(i-1)·R Rot (n g ,dA), A(i-1) is the solid model of the gear blank after the (i-1)th machining, R Rot (n g ,dA) represents the solid model of the gear blank after the (i-1)th machining process, around n g Axis rotation dA, n g Let dA be the central axis of the gear blank solid model after the (i-1)th machining, and dA be the position A(i) of the gear blank solid model during the i-th machining. 位置 ) relative to the position A(i-1) of the gear blank solid model during the (i-1)th machining operation 位置 ) about axis n g The angle of rotation is the increment of the angle of the solid model of the gear blank around the A-axis between two different machining positions; The position of the milling cutter solid model is represented as: B(i 位置 )=B(0)·T Trans (r c (i)), T Trans (r c (i) represents the solid model B(0) of the milling cutter in the machine tool coordinate system, which moves from the origin along the vector r. c (i) Move; A(i 位置 ) and B(i 位置 Perform a Boolean intersection operation to obtain the material-removed entity R(i) for the i-th processing step; 4) In the tool turret coordinate system during the i-th machining operation, according to the preset angle By repeatedly rotating the inner and outer cutter head sections at equal angles, a set H of inner cutter head sections arranged at equal angles around the cutter head axis is obtained. in and the set of external tool cross-section entities H out The inner tool section entity H, rotated j-th time, is part of the inner and outer tool section entity sets. in (i,j) and the external cutting cross-section entity H out (i,j) are subjected to Boolean intersection with the material removal entity R(i) in the i-th machining process to obtain the material removal entities of the inner and outer tools during the j-th rotation in the i-th machining process. The area extraction function module in the OpenCASCADE geometry engine is used to obtain the cutting area S of the inner tool during the j-th rotation in the i-th machining process. in (i,j) and the cutting area S of the external tool out (i,j), ； 5) By comparing the inner cutting angle, inner cutting angle, outer cutting angle, and outer cutting angle of the i-th machining process with... Based on the relationship, it can be determined whether the i-th machining operation is a single-tool cutting or multi-tool cutting, and the cutting area S of the milling cutter during the i-th machining operation can be calculated according to the cutting method. A ; In the formula N p This represents the total number of internal and external cutting teeth on the milling cutter head.

9. The method for optimizing the feed rate in milling spiral bevel gears according to claim 8, characterized in that, The determination of whether it is single-blade cutting or multi-blade cutting in step 5) is as follows: If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a single-blade cutting operation; At this point, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a multi-blade cutting operation, and the outer blade has not completely cut out when the inner blade enters the cutting operation; Angle of overlap between inner and outer blades for: ; The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining operation is determined to be a multi-blade cutting operation, and the inner blade has not yet completely cut out when the outer blade enters the cutting area; At this point, the angle of overlap between the inner and outer blades for: ; The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: ； If the internal cutting angle of the i-th machining... Angle of inner blade cutting external blade cutting angle , Angle of cut from the outside blade and The relationship is If the i-th machining is determined to be multi-blade cutting, and the inner and outer blades have overlapping areas when cutting in and out, that is, they have two overlapping cutting angles; At this point, the angle of overlap between the inner and outer blades , for: ； The overlapping cutting areas are S in,out : ； Then, the cutting area S of the milling cutter during the i-th machining operation A for: 。 10. The method for optimizing the feed rate in milling spiral bevel gears according to claim 7, characterized in that, The shear stress The formula for calculation is: , In the formula, A, B, C, n, and m are all material constants, determined based on the material properties of the gear blank. For shear strain, Shear strain rate The reference shear strain rate is T, where T is the absolute temperature. r For reference temperature, T m It is the melting temperature; The , , The calculation specifically involves: establishing a coordinate system. The y-axis coincides with the cutting edge CD, the x-axis is perpendicular to the cutting edge, the z-axis is determined by the right-hand rule, the xoz plane is defined as the normal plane, the xoy plane is defined as the cutting plane, and the plane in which the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane. The The calculation formula is , The The calculation formula is , The The calculation formula is , In the formula The average normal friction angle between the tool's rake face and the cutting plane. In the formula , It is a constant. For chip speed, For the debris angle, The angle is forward.

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