A method for predicting the cutting force of spiral bevel gears during milling

Abstract

The present invention discloses a method for predicting the cutting force of spiral bevel gear milling teeth, which comprises the following steps: Step 1, construct a blank entity model and a milling cutter entity model by using the OpenCASCADE geometric engine, and then solve the cutting area S of the milling cutter during the milling process based on the solid Boolean operation method. A ; Step 2, solve the shear stress τ of the blank by using the Johoson-Cook constitutive equation. s ; Step 3, predict the cutting force of spiral bevel gear milling teeth based on the metal oblique cutting theory: F = τ s ·S A ·(θ c1 +θ c2 +θ c3 ); 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 ); In the formula, λ s is the edge inclination angle, that is, the angle between the cutting edge and the cutting speed, φ i is the shear flow angle, φ n is the normal shear angle, θ n is the angle between the projection of the cutting force F on the normal plane and the x-axis, and the x-axis is perpendicular to the cutting edge. It can accurately obtain the cutting force during the spiral bevel gear milling process, providing a theoretical basis for subsequent milling parameter optimization and tool wear monitoring.

Description

Technical Field

[0001] The present invention relates to the technical field of spiral bevel gear milling, and particularly to a method for predicting the cutting force of spiral bevel gear milling. Background Art

[0002] During the milling process of spiral bevel gears, different process parameters will result in different cutting forces, and the cutting force affects the tooth surface quality and tool durability. Therefore, the research on cutting force is the basic work for optimizing milling parameters and monitoring tool wear.

[0003] On the basis of the relatively mature development of gear design technology and machining technology, scholars at home and abroad have carried out a large number of studies on the cutting mechanism and process parameter optimization during gear milling. Lin et al. proposed in "A Study of an Oblique Cutting Model" to use the finite element deformation analysis theory and Lagrange formula to study the oblique cutting process, constructed a finite element analysis model of oblique cutting, and verified the feasibility of the model through experiments. Sabkhi et al. obtained the cutting force coefficient in gear hobbing through a numerical model based on the geometric model of the undeformed chip generated during the hobbing process in "Characterization of the Cutting Forces Generated During the Gear Hobbing Process: Spur Gear", and analyzed the influence of cutting parameters on the machinability of materials through the variation law of cutting forces. Brecher et al. proposed an optimized model for the cutting force of generating gear grinding based on the optimization of the manufacturing process in "Approach for the Calculation of Cutting Forces in Generating Gear Grinding"; Habibi et al. proposed a parameter optimization model for face hobbing of spiral bevel gears based on the constraints of allowable cutting force and tool wear, and elaborated two cases of the successful application of this model to prove the feasibility of the model. Liu et al. used DEFORM-2D to establish a two-dimensional cutting finite element simulation model in "Optimization of Cutting / tool Parameters for Dry High-speed Spiral Bevel and Hypoid Gear Cutting with Cutting Simulation Experiment", and adopted a method combining single-factor and multi-factor orthogonal experiments to study the influence of cutting parameters and tool parameters on the cutting force during the high-speed dry cutting process of spiral bevel gears and hypoid gears. Ding et al. studied the influence of cutting parameters on the cutting force and surface roughness during the milling of cemented carbide tools in "Empirical Models and Optimal Cutting Parameters for Cutting Forces and Surface Roughness in Hard Milling of Aisi H13 Steel", and used a four-factor orthogonal experiment to measure the three cutting force components and the roughness of the machined surface, revealing that the cutting axial depth and feed rate are the main factors affecting the cutting force.

[0004] As can be seen from the above research, scholars at home and abroad have conducted sufficient research on the cutting mechanism and cutting force in milling tooth processing. By using finite element simulation analysis experiments and the principle of metal cutting, prediction models of cutting force for end mills, form mills, etc. have been established, describing the influence of process parameters and tool parameters on the cutting process; and the method of optimizing process parameters has been explored in combination with relevant cutting principles. However, the finite element simulation analysis technology adopted in these studies has a high time cost and mostly focuses on milling machining and cylindrical gear machining. Summary of the Invention

[0005] The object of the present invention is to provide a method for predicting the cutting force of spiral bevel gear milling teeth, which can accurately obtain the cutting force during the milling tooth process of spiral bevel gears and provide a theory for subsequent optimization of milling tooth parameters and tool wear monitoring.

[0006] The method for predicting the cutting force of spiral bevel gear milling teeth according to the present invention includes the following steps:

[0007] Step 1: Use the OpenCASCADE geometric engine to construct the blank entity model and the milling cutter entity model for milling teeth, and then solve based on the Boolean algorithm to obtain the cutting area S of the milling cutter during the milling tooth process A ;

[0008] Step 2: Use the Johoson-Cook constitutive equation to solve for the shear stress τ of the blank s ;

[0009] Step 3: Predict the cutting force of spiral bevel gear milling teeth based on the metal oblique cutting theory: F = τ s ·S A ·(θ c1 +θ c2 +θ c3 );

[0010] 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 );

[0011] In the formula, λ s is the inclination angle of the cutting edge, that is, the angle between the cutting edge and the cutting speed, φ i is the shear flow angle, φn is the normal shear angle, θ n is the angle between the projection of the cutting force F on the normal plane and the x-axis, and the x-axis is perpendicular to the cutting edge.

[0012] Further, the specific steps of the first step include the following steps:

[0013] 1) According to the preset gear milling parameters, calculate the cutter location point r c (i) of the milling cutter during the i-th machining, that is, the spatial position of the milling cutter in the machine tool coordinate system with the vertex of the pitch cone of the gear to be machined as the origin of the milling machine, and obtain the position vector r c of the blank corresponding to the cutter location point r g ;

[0014] 2) According to the preset blank parameters and milling cutter parameters, use the OpenCASCADE geometric engine to construct the blank solid model A(0) and the milling cutter solid model B(0) respectively;

[0015] 3) Adjust the blank solid model and the milling cutter solid model to the i-th machining position. The position of the blank solid model is expressed as:

[0016] A(i 位置 ) = A(i - 1)·R Rot (n g , dA), A(i - 1) is the blank solid model after the (i - 1)-th machining, and R Rot (n g , dA) is the blank solid model after the (i - 1)-th machining rotates by dA around the n g axis. n g is the central axis of the blank solid model after the (i - 1)-th machining, and dA is the angle of rotation of the blank solid model position A(i 位置 ) relative to the blank solid model position A(i - 1 位置 ) around the axis n g at the i-th machining, that is, the angle increment of the blank solid model around the A axis at two different machining positions;

[0017] The position of the milling cutter solid model is expressed as: B(i 位置 ) = B(0)·T Trans (r c (i)), T Trans (r c (i) means that the milling cutter solid model B(0) in the machine tool coordinate system moves along the vector r c (i) from the origin;

[0018] A(i 位置 ) and B(i 位置) Perform a Boolean intersection operation to obtain the material removal entity R(i) for the i-th machining.

[0019] 4) In the cutter head coordinate system during the i-th machining, rotate the inner and outer cutter head cross-sections at equal angles multiple times according to a preset angle to obtain a set of inner cutter cross-section entities H in and a set of outer cutter cross-section entities H out arranged at equal angles around the cutter head axis. Perform a Boolean intersection operation on the j-th rotated inner cutter cross-section entity H in (i,j) and the outer cutter cross-section entity H out (i,j) in the set of inner and outer cutter cross-section entities with the material removal entity R(i) for the i-th machining respectively, to obtain the inner and outer cutter material removal entities during the j-th rotation in the i-th machining. Use the area extraction function module in the OpenCASCADE geometric engine to obtain the inner cutter cutting area S in (i,j) and the outer cutter cutting area S out (i,j).

[0020]

[0021] 5) By comparing the inner cutter cutting-in angle, inner cutter cutting-out angle, outer cutter cutting-in angle, outer cutter cutting-out angle during the i-th machining with the relationship, determine whether the i-th machining is single-edge cutting or multi-edge cutting. Calculate the cutting area S A of the gear milling cutter during the i-th machining according to the cutting method. In the formula, N p is the total number of inner and outer cutter teeth on the gear milling cutter head.

[0022] Furthermore, the determination of single-edge cutting or multi-edge cutting in step 5) is specifically as follows: If the inner cutter cutting-in angle inner cutter cutting-out angle outer cutter cutting-in angle outer cutter cutting-out angle and the relationship is then it is determined that the i-th machining is single-edge cutting;

[0023] At this time, the cutting area S A of the gear milling cutter during the i-th machining is:

[0024]

[0025] If the inner cutter cutting-in angle inner cutter cutting-out angle outer cutter cutting-in angle outer cutter cutting-out angle and the relationship is It is determined that the i-th machining is multi-pass cutting, and when the inner tool cuts in, the outer tool has not completely cut out;

[0026] The angle at which the inner and outer tools overlap is:

[0027] The overlapping cutting area is S in,out :

[0028]

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

[0030]

[0031] If the cutting-in angle of the inner tool during the i-th machining The cutting-out angle of the inner tool The cutting-in angle of the outer tool The cutting-out angle of the outer tool and The relationship is It is determined that the i-th machining is multi-pass cutting, and when the outer tool cuts in, the inner tool has not completely cut out;

[0032] At this time, the angle at which the inner and outer tools overlap is:

[0033] The overlapping cutting area is S in,out :

[0034]

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

[0036]

[0037] If the cutting-in angle of the inner tool during the i-th machining The cutting-out angle of the inner tool The cutting-in angle of the outer tool The cutting-out angle of the outer tool and The relationship is It is determined that the i-th machining is multi-pass cutting, and there is an overlapping area when both the inner and outer tools cut in and cut out, that is, there are two overlapping cutting angles.

[0038] At this time, the angle at which the inner and outer tools overlap is:

[0039]

[0040] The overlapping cutting area is S in,out :

[0041]

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

[0043]

[0044] Furthermore, the calculation formula of the shear stress τ s is: In the formula, A, B, C, n, and m are all material constants determined according to the material characteristics of the gear blank, γ is the shear strain, is the shear strain rate, is the reference shear strain rate, T is the absolute temperature, T r is the reference temperature, T m is the melting temperature.

[0045] Furthermore, the specific calculation of φ i , φ n , and θ n in the third step is as follows: Establish a coordinate system Σ: xyz, 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 where the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane;

[0046] The calculation formula of the said φ n is

[0047] The calculation formula of the said φ i is

[0048] The calculation formula of the said θ n is θ n =β n -γ n ,

[0049] In the formula, β n is the normal average friction angle between the rake face of the tool and the cutting plane, In the formula, f 0 , p are constants, v c is the chip velocity, η λ is the chip flow angle, γ n is the normal rake angle.

[0050] By analyzing the kinematic relationship of spiral bevel gear milling, introducing the metal oblique angle cutting theory and material constitutive equation, and establishing a mathematical model of milling cutting force according to the milling cutter structure and milling motion, the milling cutting force of spiral bevel gears is accurately predicted, providing a theoretical basis for subsequent milling parameter optimization and tool wear monitoring. Brief Description of the Drawings

[0051] Figure 1 is a schematic diagram of the basic coordinate system for spiral bevel gear milling;

[0052] Figure 2 is a schematic diagram of a Gleason Phoenix type spiral bevel gear milling machine;

[0053] Figure 3 is a schematic diagram of the coordinate system for machining spiral bevel gears on a Gleason milling machine;

[0054] Figure 4 is a schematic diagram of the principle of a single-edge oblique angle cutting model;

[0055] Figure 5 is a schematic diagram of the direction of the cutting force and cutting speed in oblique angle cutting;

[0056] Figure 6 is a comparison chart of the actually measured cutting force and the predicted cutting force under the first test condition;

[0057] Figure 7 is a comparison chart of the actually measured cutting force and the predicted cutting force under the second test condition. Detailed Embodiment

[0058] The present invention will be described in detail below with reference to the accompanying drawings.

[0059] A method for predicting the milling cutting force of spiral bevel gears includes the following steps:

[0060] Step 1: Use the OpenCASCADE geometric engine to construct the blank solid model and the milling cutter solid model, and then solve for the cutting area S of the milling cutter during the milling process based on the solid Boolean operation method A , which specifically includes the following steps:

[0061] 1) Refer to Figure 1 , establish the basic coordinate system for spiral bevel gear milling, is the static coordinate system fixed to the ground. is the machine tool processing coordinate system, and the origin O is located on the axis of the rotating table. is in the horizontal cross-section of the rotating table, and the coordinate plane is perpendicular to the axis of the rotating table, and the normal vector of this plane is parallel to the axis of the rotating table and points outside the rotating table. is the cutter head coordinate system fixed to the milling cutter, with the origin O c located on the rotation axis of the milling cutter and being the spatial position control point of the milling cutter. The radial vector is the vector position of the milling cutter coordinate system in Σ. The coordinate plane is coplanar with the coordinate plane of Σ . Then, make an axial section of the generating surface through the tip point P and establish a frame coordinate system O o coincides with O c , points from O o to point P, coincides with in Σ, is the rotation axis of the milling cutter. Before the cutter tilt body is adjusted, is in the same direction as c in Σ . In the figure, X p is the horizontal wheel position correction amount, X b is the bed position, E m is the vertical wheel position, S is the cutter position, Γ is the machine tool installation root cone angle, j 0 is the cutter tilt direction angle, i 0 is the basic cutter tilt angle, q s is the starting indexing table angle, q e is the ending indexing table angle, q t is the angle between the line connecting the center O c of the cutter head at any moment to the center O of the indexing table and .

[0062] From the figure, the representation of the vector from the vertex G of the workpiece pitch cone, i.e., the shaft intersection point, to the center of the milling cutter in the machine tool machining coordinate system Σ is: In the formula, is the workpiece axis vector, is the angular cutter position of the milling cutter, and they are respectively expressed as: In the formula, q t is the angle between the line connecting the center O c of the cutter head at any moment to the center O of the indexing table and .

[0063] The representation of the cutter axis vector in the machining coordinate system is: In the formula, j 0 is the cutter tilt direction angle, i 0 is the basic cutter tilt angle, represents the transformation matrix of a certain vector rotating by an angle i around the vector 0 .

[0064] To achieve the relative position and relative motion between the milling cutter and the workpiece, a mechanical milling machine uses a swivel table mechanism to adjust the distance between the center of the milling cutter and the center of the swivel table; through the eccentric mechanism and the cutter tilt / rotation body adjustment, the angle adjustment between the axis of the milling cutter and the axis of the swivel table and between the axis of the cutter head and the tilt direction is realized. However, due to the complex structure of the swivel table mechanism and the cutter tilt body, the adjustment is cumbersome. In order to simplify the machine tool structure, Gleason milling machines abandon the swivel table structure and cutter tilt device of mechanical machine tools. For its basic model, see Figure 2 , as can be seen from the figure, the milling machine mainly includes three linear linear axes, namely the X, Y, and Z axes, three rotary axes, namely the A, B, and C axes, as well as the bed and the rotary table, with a total of six degrees of freedom; among them, the A axis is the workpiece rotation spindle, and the C axis is the milling cutter rotation spindle; the B axis is the rotary table rotating around the Y axis, mainly changing the angle between the workpiece spindle and the tool spindle.

[0065] See Figure 3 , establish the coordinate system for Gleason milling machines to machine spiral bevel gears. The coordinate system Σ={O,x,y,z} is the machine tool processing coordinate system fixedly connected to the machine tool; the coordinate system Σ p ={O p ,x p ,y p ,z p} is fixedly connected to the gear blank. The origin O p is separated from the origin of the machine tool coordinate system by x e , x e is a constant, and the angle between the x p axis and the x axis in the machine tool coordinate system is Γ, that is, the machine tool installation root cone angle. The coordinate system Σ c ={O c ,x c ,y c ,z c} is fixedly connected to the milling cutter. The z c axis is parallel to the z axis of the machine tool coordinate system. [x(O),y(O),z(O)] represents the spatial position of the origin O c of the milling cutter coordinate system in the machine tool coordinate system.

[0066] For the swivel table, the three-axis simultaneous interpolation motions x(O), y(O), z(O) along the X, Y, and Z axes are used to replace it in the milling machine. At the same time, the machine tool adjustment parameters (horizontal wheel position, vertical wheel position, and bed position) are converted into the motions of three linear linear axes. The rotation of the workpiece corresponds to the rotation around the A axis in the milling machine, and the machine tool installation root cone angle corresponds to the rotation around the B axis in the milling machine. For the cutter tilt / rotation device, the milling machine compensates the inclination angle of the axis of the milling cutter into the motions of the A axis and the B axis, and realizes the numerical control generating milling motion of spiral bevel gears through five-axis simultaneous motion.

[0067] Therefore, to calculate the cutter location points in the gear milling machine, it is necessary to first calculate the additional motions of the A-axis and B-axis caused by the cutter tilt. The calculation formulas for the rotation angle dA around the A-axis and the rotation angle dB around the B-axis are respectively expressed as:

[0068] In the formula

[0069] Taking the vertex of the workpiece pitch cone as the origin of the gear milling machine, the motion trajectories of each coordinate axis during the gear milling process are as follows:

[0070]

[0071] In the formula, V ls is the relative position vector between the workpiece and the gear milling cutter after the additional motion The representation in the static coordinate system is:

[0072] Raq is the machine tool gear ratio; q t is the final indexing table angle, and q s is the starting indexing table angle.

[0073] According to the preset gear milling processing parameters, the cutter location point r c (i) is calculated, that is, the spatial position of the gear milling cutter in the machine tool coordinate system with the vertex of the gear to be machined's pitch cone as the origin of the gear milling machine. r c (i) = [x c (i), y c (i), z c (i)], where x(i), y(i), and z(i) represent the position distances of the origin of the gear milling cutter coordinate in the machine tool coordinate system. The axis vector of the gear milling cutter is parallel to the z-axis of the machine tool coordinate system as: n c = [0, 0, 1].

[0074] And the position vector r c of the blank corresponding to the cutter location point r g is obtained. = [x g (i), y g (i), z g (i)], where x g (i), y g (i), z g (i) represent the position distances of the origin of the blank coordinate system in the machine tool coordinate system, which are usually fixed values. The angle between the blank axis and the x-axis of the machine tool coordinate system is adjusted by the B-axis as: n g = [1, 0, 0]·M(z, Γ).

[0075] M(z, Γ) represents the rotation matrix of rotating an angle Γ around the z-axis and is expressed as:

[0076] 2) Construct the blank entity model A(0) and the milling cutter entity model B(0) respectively using the OpenCASCADE geometric engine according to the preset blank parameters and milling cutter parameters.

[0077] 3) Adjust the blank entity model and the milling cutter entity model to the i-th machining position. The position of the blank entity model is expressed as:

[0078] A(i 位置 ) = A(i - 1)·R Rot (n g , dA), where A(i - 1) is the blank entity model after the (i - 1)-th machining, and R Rot (n g , dA) is the blank entity model after the (i - 1)-th machining rotated by dA around the n g axis. n g is the central axis of the blank entity model after the (i - 1)-th machining, and dA is the angle of rotation of the blank entity model position A(i 位置 ) relative to the blank entity model position A(i - 1 位置 ) around the axis n g at the i-th machining, that is, the angle increment of the blank entity model around the A axis at two different machining positions.

[0079] The position of the milling cutter entity model is expressed as: B(i 位置 ) = B(0)·T Trans (r c (i)), where T Trans (r c (i) is the movement of the milling cutter entity model B(0) from the origin along the vector r c (i) in the machine tool coordinate system.

[0080] Perform a Boolean intersection operation on A(i 位置 ) and B(i 位置 ) to obtain the blank entity model A(i) after the i-th machining, which is expressed as:

[0081] A(i) = A(i 位置 ) - B(i 位置 ).

[0082] Perform a Boolean intersection operation on A(i 位置 ) and B(i 位置 ) to obtain the removed material entity R(i) after the i-th machining, which is expressed as:

[0083] R(i) = A(i 位置 ) ∩ B(i 位置 ).

[0084] In the cutter head coordinate system during the i-th machining, at a preset angle Rotate the inner and outer cutter sections at equal angles multiple times to obtain a set of inner cutter section entities H arranged at equal angles around the cutter head axis in and a set of outer cutter section entities H out , expressed as:

[0085] where H in (i,j) is the inner cutter section entity after the inner cutter section entity rotates j times during the i-th machining, and H in (0) is the initial inner cutter section entity, is the initial inner cutter section entity rotating around the milling cutter head axis n c by T Trans (r c (i)) is the initial inner cutter section entity moving from the origin along the vector r c (i).

[0086] where H out (i,j) is the outer cutter section entity after the outer cutter section entity rotates j times during the i-th machining, and H out (0) is the initial outer cutter section entity, is the initial outer cutter section entity rotating around the milling cutter head axis n c by T Trans (r c (i)) is the initial outer cutter section entity moving from the origin along the vector r c (i).

[0087] Perform a Boolean intersection operation on H in (i,j) and H out (i,j) with the material removal entity R(i) during the i-th machining respectively to obtain the inner and outer cutter material removal entities during the j-th rotation in the i-th machining. Use the area extraction function module in the OPENCASCADE geometric engine to obtain the inner cutter cutting area S in (i,j) and the outer cutter cutting area S out (i,j), expressed as:

[0088]

[0089] 5) By comparing the inner cutter cutting-in angle, inner cutter cutting-out angle, outer cutter cutting-in angle, outer cutter cutting-out angle during the i-th machining with the relationship, determine whether the i-th machining is single-edge cutting or multi-edge cutting; where N p is the total number of inner and outer cutter teeth on the milling cutter head.

[0090] Inner tool cutting-in angle for the i-th machining Inner tool cutting-out angle Outer tool cutting-in angle Outer tool cutting-out angle Expressed as:

[0091]

[0092] In the formula, min(H in (i, {1, 2, 3,... j,...}) ∩ R(i), j) represents the rotation angle corresponding to the inner tool cross-section H in (i, j) with the smallest rotation angle in the intersection of the removed material R(i) during the i-th machining;

[0093] max(H in (i, {1, 2, 3,... j,...}) ∩ R(i), j) represents the rotation angle corresponding to the inner tool cross-section H in (i, j) with the largest rotation angle in the intersection of the removed material R(i) during the i-th machining.

[0094] min(H out (i, {1, 2, 3,..., j,...}) ∩ R(i), j) represents the rotation angle corresponding to the outer tool cross-section H out (i, j) with the smallest rotation angle in the intersection of the removed material R(i) during the i-th machining;

[0095] max(H out (i, {1, 2, 3,... j,...}) ∩ R(i), j) represents the rotation angle corresponding to the outer tool cross-section H out (i, j) with the largest rotation angle in the intersection of the removed material R(i) during the i-th machining.

[0096] The judgment of single-edge cutting or multi-edge cutting is specifically as follows:

[0097] ① If the inner tool cutting-in angle for the i-th machining Inner tool cutting-out angle Outer tool cutting-in angle Outer tool cutting-out angle And The relationship is Then it is determined that the i-th machining is single-edge cutting.

[0098] At this time, the cutting area S of the milling cutter during the i-th machining A Is:

[0099]

[0100] ② If the cutting-in angle of the inner tool in the i-th machining Cutting-out angle of the inner tool Cutting-in angle of the outer tool Cutting-out angle of the outer tool and The relationship is Then it is determined that the i-th machining is multi-tool cutting and only one stage overlaps, that is, when the inner tool cuts in, the outer tool has not completely cut out.

[0101] The overlapping angle of the inner and outer tools is:

[0102] The overlapping cutting area is S in,out :

[0103]

[0104] Then the cutting area S of the gear milling cutter during the i-th machining A is:

[0105]

[0106] ③ If the cutting-in angle of the inner tool in the i-th machining Cutting-out angle of the inner tool Cutting-in angle of the outer tool Cutting-out angle of the outer tool and The relationship is Then it is determined that the i-th machining is multi-tool cutting and only one stage overlaps, that is, when the outer tool cuts in, the inner tool has not completely cut out.

[0107] At this time, the overlapping angle of the inner and outer tools is:

[0108] The overlapping cutting area is S in,out :

[0109]

[0110] Then the cutting area S of the gear milling cutter during the i-th machining A is:

[0111]

[0112] ④ If the cutting-in angle of the inner tool in the i-th machining Cutting-out angle of the inner tool Cutting-in angle of the outer tool Cutting-out angle of the outer tool and The relationship is It is determined that the i-th machining is multi-pass cutting, and there is an overlapping area when the inner tool and the outer tool enter and exit the workpiece.

[0113] At this time, the overlapping angle of the inner and outer tools is:

[0114]

[0115] The overlapping cutting area is S in,out :

[0116]

[0117] Then, during the i-th machining, the cutting area S of the gear milling cutter A is:

[0118]

[0119] Step 2: Solve the shear stress τ of the gear blank using the Johoson-Cook constitutive equation s , and the calculation formula for the shear stress τ s is: In the formula, A, B, C, n, and m are all material constants determined according to the material characteristics of the gear blank, γ is the shear strain, is the shear strain rate, is the reference shear strain rate, T is the absolute temperature, T r is the reference temperature, T m is the melting temperature.

[0120] In this embodiment, the material of the gear blank is 20CrMnTi, and the values of each constant and thermophysical property parameter are shown in Table 1.

[0121] Table 1 J-C constitutive model material constants of material 20CrMnTi

[0122] Material A B C n m <![CDATA[γ 0 > <![CDATA[T m (℃)]]> <![CDATA[T r (℃)]]> <![CDATA[ρ (kg / m 3 )]]> c (J / kg K) μ 20CrMnTi 720 712 0.01 0.68 1.0 0.001 1800 300 7800 460 0.85

[0123] Step 3: During the metal cutting process, the material of the cutting layer is pushed by the rake face to form a chip and separates from the workpiece. In order to establish a mechanical model of the chip in this process, the process of changing the cutting layer material into a chip is usually regarded as a plastic shear deformation process that occurs when the material passes through a single shear plane. Therefore, the resultant force of the internal forces on the shear plane and the resultant force of the external forces on the tool-chip contact surface satisfy the static equilibrium condition, and the cutting force during the cutting process is obtained through mechanical analysis.

[0124] Predict the milling cutting force of spiral bevel gears based on the metal oblique cutting theory: F = τ s ·S A ·(θ c1 +θ c2 +θc3 )

[0125] θ c 1 = 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 )

[0126] where λ s is the rake angle, i.e., the angle between the cutting edge and the cutting speed, φ i is the shear flow angle, φ n is the normal shear angle, θ n is the angle between the projection of the cutting force F on the normal plane and the x-axis, and the x-axis is perpendicular to the cutting edge.

[0127] See Figure 4 , in the oblique cutting model, establish a coordinate system ∑: xyz, 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 where the cutting material layer undergoes three-dimensional plastic deformation is defined as the shear plane. represents the cutting speed. represents the chip flow velocity; measure the angle γ n between the rake face of the tool and the z-axis in the normal plane, and it is defined as the normal rake angle; the angle η λ between the chip flow velocity and OA (perpendicular to the cutting edge CD) in the normal plane is defined as the chip flow angle; λ s is defined as the rake angle, φ n is defined as the normal shear angle.

[0128] See Figure 5 , in the shown oblique cutting, the cutting force and the cutting speed. In the figure, F is the cutting force (opposite to the cutting speed direction ), F n is the normal force on the shear plane, F s is the shear stress on the shear plane; F c is the main cutting force, F d is the back resistance, F f is the feed force; φ i is the shear flow angle, φ n is the normal shear angle, θ nIt is the angle between the projection of the cutting force F on the normal plane and the x-axis.

[0129] The φ i , φ n , θ n are calculated specifically as follows:

[0130] The calculation formula for the φ n is

[0131] The calculation formula for the φ i is

[0132] The calculation formula for the θ n is θ n =β n -γ n ,

[0133] In the formula, β n is the normal average friction angle between the rake face of the cutting tool and the cutting plane, In the formula, f 0 , p are constants, v c is the chip velocity, η λ is the chip flow angle, γ n is the normal rake angle.

[0134] Chip velocity In the formula, n is the rotational speed of the gear milling cutter, d CD is the nominal diameter of the gear milling cutter.

[0135] In order to verify the mathematical model of the gear milling cutting force, an actual gear milling experiment was completed using the YKH2235 CNC spiral bevel gear milling machine produced by Tianjin No. 1 Machine Tool General Factory. The spiral bevel gear blank parameters, milling machine adjustment parameters, and rough gear milling cutter parameters in the actual gear milling experiment are shown in Tables 2 to 4 respectively.

[0136] Table 2 Spiral bevel gear blank parameters

[0137] Parameter / Unit Value Parameter / Unit Value Number of teeth 11 Face cone angle / ° 23.9 Module 4.024 Pitch cone angle / ° 19.7 Tooth width / mm 27.64 Distance between pitch cone apex and axis intersection point / mm 1.4 Helical direction Left - hand Distance between root cone apex and axis intersection point / mm -1.22 Helix angle / ° 49.8 Distance between face cone apex and axis intersection point / mm 0.38 Theoretical whole tooth height / mm 8.02 Distance from crown to axis intersection point / mm 79.25 Root cone angle / ° 18.9 Distance from front crown to axis intersection point / mm 53.98

[0138] Table 3 Milling machine adjustment parameters

[0139] Parameter / Unit Value Parameter / Unit Value Horizontal wheel position / mm 1.78 Machine tool installed root cone angle / ° 18.9 Bed position / mm -0.97 Starting indexing head angle / ° 48.51012 Vertical wheel position / mm 23.86 End indexing head angle / ° 86.04795 Radial tool position / mm 69.86 Basic indexing head angle / ° 67.61651 Ratio of rolling 4.09179

[0140] Table 4 Rough gear milling cutter parameters

[0141] Parameter / Unit Value Nominal diameter of cutter head / mm 127 Profile angle of external cutter teeth / ° 14 Profile angle of internal cutter teeth / ° 24 Tip stagger of internal and external cutter teeth / mm 2.54 Tip rounding radius of cutter teeth / mm 0.99

[0142] The gear milling cutter is a rough cutting cutter head from Harbin Tool Works, with eight inner and outer blades, a total of sixteen blades. The blade material is high-speed steel, the rake angle is 20°, and the cutting edge inclination angle is 5°. The blank material is 20CrMnTi, and the cutting cooling method is oil bath cooling.

[0143] One end of the rotor of the rotary dynamometer is connected to the milling machine spindle through a spindle adapter, and the other end is connected to the cutter head through a customized cutter head adapter; the stator is fixed to the spindle end face by a self-made simple bracket and connected to the signal collector using a high-insulation impedance cable to achieve signal transmission; the relevant parameters of the dynamometer are set and the cutting force analysis during the cutting process is displayed through DynoWare software on a laptop. In order to expand the application range of the cutting force calculation model and considering the limitations of the machine tool mechanical structure. Experiments were carried out for two different milling cutting conditions respectively:

[0144] The first condition: The cutter head cuts from the basic cradle angle position to the theoretical full tooth height. At this time, the blank is fixed and there is no generating motion between the cutter head and the blank. The cutting situation between the two is similar to form milling.

[0145] The second condition: The cutter head starts cutting from the starting cradle angle and generates from the large end to the small end. At this time, there is a generating motion between the cutter head and the blank.

[0146] When milling teeth, the cutter head speed is 120 r / min, the feed speed is 30 mm / min when cutting from the basic cradle angle, and the feed speed is 36 mm / min when cutting from the starting cradle angle. The RCD calculation function in Kistler was used in this experiment. This function can obtain the tangential cutting force of the milling cutter by inputting the cutter diameter. The cutting process data collected is based on the processing time, and the experimental data in the time intervals of [23, 37] seconds and [32, 78] seconds were intercepted respectively. At the same time, the cutting force prediction results of the two test conditions were obtained by using the above-mentioned spiral bevel gear milling cutting force prediction method. In the milling cutter coordinate system, a comparison chart of the actually measured cutting force and the predicted cutting force under the two experimental conditions was drawn.

[0147] See Figure 6, the horizontal axis is the cutting time, the vertical axis is the tangential cutting force during the cutting process, the solid line is the actual measurement result, and the dotted line is the predicted result. It can be seen from the figure that the predicted tangential cutting force rises rapidly in the pre-cutting stage, rises more steadily in the middle stage, and tends to be stable in the later stage. The cutting force change trend is basically consistent with the actual measurement result. However, there are certain differences in the cutting force values. The main factors affecting the error are: the cutting force calculation model itself has errors. From the verification of the bevel cutting force model, it can be found that as the cutting thickness increases, the cutting error tends to increase; due to the machine tool mechanism and the installation method of the dynamometer, the rigidity of the cutter head is weak, which makes the deformation of the cutter head larger and the runout deviation of the cutter head increase during the cutting process; the error between the cutter head cutting edge radius, material friction factor and shear thickness of the shear zone and the actual value, etc. In order to solve this problem, the cutting force coefficient calibration experiment can be carried out first to calibrate the correlation coefficient, which can effectively reduce the error between the cutting force prediction value and the experimental value. However, the process is complicated and cumbersome, and the main purpose of the present invention is to verify the cutting force change trend during the gear milling process, and to optimize the cutting process parameters by predicting the cutting force change trend. Therefore, the cutting force coefficient calibration is omitted in this experiment. Therefore, from the comparison analysis diagram of the predicted value and the experimental value, it can be concluded that the tangential cutting force change trend predicted by the present invention has a good consistency with the tangential cutting force change trend during the actual cutting process, indicating that the model can better reflect the change trend of the tangential cutting force during the gear milling process.

[0148] See also Figure 7 , the predicted tangential cutting force increases rapidly to the maximum value in the early stage of development and cutting, and gradually decreases after reaching the peak value. In the post-cutting stage, the cutting force decreases rapidly. This change trend is basically the same as the change trend of the actual measurement results. However, it can be seen from the figure that there is a certain error in the values ​​of the two. The main influencing factors of this error are basically the same as the error influencing factors when cutting from the basic cradle angle; the predicted tangential cutting force peak time is a little earlier than the experimentally measured tangential cutting force peak time. The reason for this phenomenon may be: due to the existence of the dynamometer, the cutter head is in a state of overhanging too long, and the whole is a cantilever beam model with poor rigidity. In the cutting process, the milling cutter is impacted by the cutting force. The tool deformation and runout error increase, which makes the milling cutter tend to move outward, resulting in a reduction in the cutting thickness in this cutting; when predicting the tangential cutting force, the cutting edge of the milling cutter is regarded as absolutely sharp and rigid, and the runout error of the milling cutter is not considered. Therefore, when the predicted value of the tangential cutting force reaches the peak value, the experimental value has not reached the peak value, but the changing trends of the tangential cutting force are basically consistent during the entire cutting process. The changing trend of the predicted value of the tangential cutting force can better reflect the changing trend of the experimental value.

[0149] After observation and comparison, the cutting area position, cutting area shape, and cutting results of the simulated cutting and actual cutting in OCC are basically the same under the two cutting conditions, and the simulated cutting process can better reflect the actual cutting process.

[0150] The above are only the preferred embodiments of the present invention and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for predicting the cutting force of spiral bevel gear milling, characterized in that, it includes the following steps: Step 1: Use the OpenCASCADE geometric engine to construct the solid model of the blank and the solid model of the milling cutter, and then solve for the cutting area S of the milling cutter during the milling process based on the solid Boolean operation method A ; Specifically, it includes the following steps: 1) Calculate the cutter location point \(r(i)\) of the gear milling cutter during the \(i\)-th machining according to the preset gear milling machining parameters, that is, the spatial position of the gear milling cutter in the machine tool coordinate system with the vertex of the pitch cone of the gear to be machined as the origin of the gear milling machine, and obtain the position vector \(r\) of the blank corresponding to the cutter location point \(r(i)\); c (i), namely, in the machine tool coordinate system with the vertex of the pitch cone of the gear to be machined as the origin of the gear milling machine, the spatial position of the gear milling cutter, and obtain the position vector \(r\) of the blank corresponding to the cutter location point \(r(i)\); c (i); g ; 2) According to the preset blank parameters and milling cutter parameters, use the OpenCASCADE geometric engine to construct the blank solid model A(0) and the milling cutter solid model B(0) respectively; 3) Adjust the blank solid model and the milling cutter solid model to the i-th machining position. The position of the blank solid model is expressed as: A(i 位置 ) = A(i - 1)·R Rot (n g , dA), where A(i - 1) is the blank solid model after the (i - 1)-th machining, and R Rot (n g , dA) is the blank solid model after the (i - 1)-th machining rotated by dA about the axis n g . n g is the central axis of the blank solid model after the (i - 1)-th machining, and dA is the angle by which the blank solid model at position A(i 位置 ) rotates about the axis n 位置 relative to the blank solid model at position A(i - 1 g ) during the i-th machining, that is, the angular increment of the blank solid model at two different machining positions about the axis A; The position of the milling cutter solid model is expressed as: B(i 位置 ) = B(0)·T Trans (r c (i)), T Trans (r c (i) is the movement of the milling cutter solid model B(0) from the origin along the vector r c (i); A(i 位置 ) and B(i 位置 ) are subjected to a Boolean intersection operation to obtain the material removal entity R(i) for the i-th machining. 4) In the cutter head coordinate system during the i-th machining, rotate the inner and outer cutter head cross-sections at equal angles multiple times to obtain a set of inner cutter cross-section entities H arranged at equal angles around the cutter head axis in and a set of outer cutter cross-section entities H out . For the inner cutter cross-section entity H in (i, j) and the outer cutter cross-section entity H out (i, j) rotated for the j-th time in the inner and outer cutter cross-section entity sets respectively, perform a Boolean intersection operation with the material removal entity R(i) during the i-th machining to obtain the inner and outer cutter material removal entities during the j-th rotation in the i-th machining. Use the area extraction function module in the OpenCASCADE geometric engine to obtain the inner cutter cutting area S in (i, j) and the outer cutter cutting area S out (i, j). 5) By comparing the inner tool cutting-in angle, inner tool cutting-out angle, outer tool cutting-in angle, and outer tool cutting-out angle during the i-th machining with the relationship, it is determined whether the i-th machining is single-tool cutting or multi-tool cutting, and the cutting area S of the gear milling cutter during the i-th machining is calculated according to the cutting method A ; where N p is the total number of inner and outer tool teeth on the gear milling cutter disk; Step 2: Solve using the Johoson-Cook constitutive equation to obtain the shear stress τ of the gear blank s ; Step 3, predicting the cutting force of spiral bevel gear milling based on the metal oblique cutting theory: F = τ s ·S A ·(θ c1 + θ c2 + θ c3 ); 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 ); where λ s is the inclination angle of the cutting edge, that is, the angle between the cutting edge and the cutting speed, φ i is the shear flow angle, φ n is the normal shear angle, θ n is the angle between the projection of the cutting force F on the normal plane and the x-axis, and the x-axis is perpendicular to the cutting edge.

2. The method for predicting the cutting force of spiral bevel gear milling according to claim 1, characterized in that, the judgment of single-edge cutting or multi-edge cutting in step 5) is specifically: If the cutting-in angle of the internal tool for the i-th machining Cutting-out angle of the internal tool Cutting-in angle of the external tool Cutting-out angle of the external tool And The relationship is Then it is determined that the i-th machining is single-point cutting; At this time, the cutting area S of the milling cutter during the i-th machining A is as follows: If the cutting-in angle of the inner tool in the i-th machining Cutting-out angle of the inner tool Cutting-in angle of the outer tool Cutting-out angle of the outer tool And The relationship is Then it is determined that the i-th machining is multi-tool cutting, and the outer tool has not completely cut out when the inner tool cuts in; The angle of coincidence between the inner and outer knives is: The overlapping cutting area is S in,out : Then, during the i-th machining, the cutting area S of the milling cutter A is as follows: If the cutting-in angle of the inner tool for the i-th machining cutting-out angle of the inner tool cutting-in angle of the outer tool cutting-out angle of the outer tool and the relationship is then it is determined that the i-th machining is multi-pass cutting, and the inner tool has not completely cut out when the outer tool cuts in; The angle at which the inner and outer knives coincide at this time is as follows: The overlapping cutting area is S in,out : Then, during the i-th machining, the cutting area S of the milling cutter A is as follows: If the cutting-in angle of the inner tool in the i-th machining Cutting-out angle of the inner tool Cutting-in angle of the outer tool Cutting-out angle of the outer tool And The relationship is Then it is determined that the i-th machining is multi-tool cutting, and there is an overlapping area when the inner tool and the outer tool cut in and cut out, that is, there are two overlapping cutting angles; The angle at which the inner and outer knives coincide at this time is: The overlapping cutting area is S in,out : Then, during the i-th machining, the cutting area S of the milling cutter A is as follows:

3. The method for predicting the cutting force of spiral bevel gear milling according to claim 1, characterized in that, The shear stress τ s is calculated by the following formula: where A, B, C, n, and m are all material constants determined according to the material properties of the gear blank, γ is the shear strain, is the shear strain rate, is the reference shear strain rate, T is the absolute temperature, T r is the reference temperature, and T m is the melting temperature.

4. The method for predicting the cutting force of spiral bevel gear milling according to claim 1, characterized in that, In step three, the calculation of φ i , φ n , θ n is specifically 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 where the three-dimensional plastic deformation of the cutting material layer occurs is defined as the shear plane; The described φ n The calculation formula is The φ i is calculated as The said θ n The calculation formula of θ n =β n -γ n , where β n is the normal average friction angle between the rake face of the cutting tool and the cutting plane, where f 0 , p are constants, v c is the chip velocity, η λ is the chip flow angle, γ n is the normal rake angle.

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