Calculation method of grinding wheel diameter for gear hobbing cutter based on Archimedean spiral relationship

Abstract

The present invention relates to a method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship. The method establishes a three-dimensional model of a gear hobbing cutter spiral and combines the Archimedean spiral to reversely calculate the spatial relationship between the back face of the front row of gear hobbing cutter teeth and the grinding wheel, thereby ensuring that the grinding wheel will not interfere with the back row of gear hobbing cutter teeth when processing to the end of the front row of gear hobbing cutter teeth. The specific steps include: generating the helix of the gear hobbing cutter and its three-dimensional model according to the geometric parameters of the gear hobbing cutter; obtaining the spatial curve of the tip of the back row of gear hobbing cutter teeth and the spatial curve of the tip of the front row of gear hobbing cutter teeth, calculating the Archimedean spiral cluster of the back face of the gear hobbing cutter, and determining the maximum diameter of the grinding wheel by calculating the normal vector of the interference-prone position of the back face of the front row of gear hobbing teeth. The method effectively improves the calculation accuracy of the grinding wheel diameter, avoids the interference problem in the gear hobbing cutter processing process, and ensures the processing quality and efficiency.

Description

Technical Field

[0001] The invention relates to the field of mechanical processing, in particular to a method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship, which is used for accurately determining the maximum effective diameter of a grinding wheel used in the process of machining a gear hobbing cutter. Background Art

[0002] In modern manufacturing, gears are widely used in many fields such as automobiles, aerospace, and engineering machinery. The accuracy and quality of gears are crucial to the operating performance of mechanical equipment. As the core tool for gear processing, the geometric accuracy of the gear hobbing cutter directly affects the processing quality of the gear. The manufacturing of the gear hobbing cutter requires extremely high precision to ensure its performance in gear processing. The grinding wheel plays a vital role in this process and is a key tool for manufacturing gear hobbing cutters, which directly affects the geometry and surface quality of the gear hobbing cutter. The reasonable determination of the maximum diameter of the grinding wheel not only determines the machining accuracy of the first row of hobbing teeth, but more importantly, ensures that the grinding wheel will not interfere with the rear row of hobbing teeth when processing to the end of the first row of hobbing teeth. The occurrence of interference will cause damage to the gear hobbing cutter and even lead to the failure of the entire processing process. At the same time, the smaller the diameter of the grinding wheel means the easier the process of manufacturing the grinding wheel, and the production of grinding wheels below 40 mm in diameter is more difficult. Therefore, the maximum diameter of the grinding wheel must be accurately calculated to ensure that the grinding wheel can work effectively in the complex geometry of the gear hobbing cutter without affecting other unprocessed parts.

[0003] Traditional methods for calculating grinding wheel diameter are usually based on experience or simple geometric deduction. However, due to the complex shape of the gear hobbing cutter, the variable relative position relationship of each row of hobbing teeth, and the difficulty in calculating the Archimedean spiral of the back hobbing cutter face, the traditional method cannot guarantee the accuracy of the calculation. This not only easily leads to interference problems during processing, but also may affect the overall manufacturing accuracy of the gear hobbing cutter and the quality of the gear produced in the end. Summary of the invention

[0004] In order to solve the above problems, a method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship is proposed. The method of the present invention models and simulates the relative position relationship between the gear hobbing cutter and the grinding wheel, inversely calculates the Archimedean spiral of the back face of the gear hobbing cutter, and accurately calculates the maximum effective diameter required by the grinding wheel during the processing. This method can ensure that when processing to the end of the previous row of hobbing teeth, the grinding wheel will not interfere with the back row of teeth of the gear hobbing cutter. The present invention overcomes the shortcomings of traditional methods and can efficiently and accurately calculate the maximum diameter of the grinding wheel required for processing gear hobbing cutters, which not only improves the manufacturing precision of gear hobbing cutters, but also reduces the potential risks in gear hobbing cutter processing, providing an efficient and reliable technical solution for the gear manufacturing industry.

[0005] The present invention is implemented by the following technical solutions:

[0006] A method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship comprises the following steps:

[0007] Step 1: Given the geometric parameters of the gear hobbing cutter, including the outer diameter of the gear hobbing cutter, grinding length, relief amount, helix angle, number of chip grooves, tool edge shape, chip groove lead and other related geometric parameters.

[0008] Step 2: Construct a three-dimensional model of the gear hobbing cutter spiral, specifically:

[0009] Firstly, the helical line of the gear hobbing cutter is established and generated according to the given geometric parameters of the gear hobbing cutter;

[0010] Then, the gear hobbing cutter spiral line and the gear hobbing cutter tool edge shape are combined through translation and rotation to generate a gear hobbing cutter spiral three-dimensional model.

[0011] Step three: Obtain the spatial curve of the tip of the rear row teeth and the spatial curve of the tip of the front row teeth of the gear hobbing cutter, specifically: perform coordinate transformation on the spiral three-dimensional model of the gear hobbing cutter and extract the spatial curve of the tip of the rear row teeth of the gear hobbing cutter through interpolation processing, wherein the spatial curve of the tip of the rear row teeth of the gear hobbing cutter includes the spatial curve of the back of the rear row teeth and the spatial curve of the back of the rear row teeth; based on the tool blade shape of the gear hobbing cutter, the spatial curve of the tip of the front row teeth is obtained according to mathematical modeling software.

[0012] Step 4: Calculate the Archimedean spiral cluster of the gear hobbing cutter flank, specifically: calculate the Archimedean spiral cluster of the gear hobbing cutter flank under a given backing amount according to the space curve of the front row tooth tips and the space curve behind the back row teeth.

[0013] Step 5: Perform coordinate transformation and interpolation processing on the Archimedean spiral cluster on the back face of the gear hobbing cutter to obtain the end space curve of the back face of the front row of gear hobbing cutter teeth, so as to obtain the grinding wheel exit position of the front row of gear hobbing cutter teeth in the final stage of back grinding.

[0014] Step six: Based on the spatial curve at the end of the back face of the front row of teeth of the gear hobbing cutter and the Archimedean spiral cluster on the back face of the gear hobbing cutter, calculate the intersection normal vector of the Archimedean spiral at the end of the back face of the front row of teeth of the gear hobbing cutter; since the normal vector of the machined surface must pass through the center of rotation of the tool during the machining process of the rotating tool, by calculating the intersection normal vector between the final cutting position of the grinding wheel and the back face of the gear hobbing cutter, the position of the center of the grinding wheel in the final stage of machining can be determined, specifically on the extension line of the intersection normal vector.

[0015] Step seven: Calculate the maximum diameter of the grinding wheel (space circumscribed circle method). The specific method is: based on the above calculation results (intersection normal vector, the spatial curve of the end of the back face of the front row of gear hobbing teeth, and the spatial curve of the back row of gear hobbing teeth without back relief), calculate the perpendicular surface between the spatial curve of the end of the back face of the front row of gear hobbing teeth and the spatial curve of the back row of gear hobbing teeth without back relief. By calculating the intersection of the intersection normal vector and the perpendicular surface, the final grinding wheel center position is obtained. The minimum distance between the center and the end of the back face of the front row of gear hobbing teeth is the maximum diameter of the grinding wheel without interference.

[0016] Preferably, in step 2, the rotation matrix R is used x The tool edge shape of the gear hobbing cutter t 0 The three-dimensional spiral surface of the gear hobbing cutter is rotated and translated to given geometric parameters to obtain a three-dimensional spiral model of the gear hobbing cutter.

[0017] Preferably, the calculation of the gear hobbing cutter helix l1 is as shown in formula (1):

[0018] (1)

[0019] Among them, (l1X i , l1Y i , l1Z i ) represents the coordinates of the helical line of the gear hobbing cutter, It represents the X-axis value corresponding to point i on the curve obtained by linearly growing the spiral line with the X-axis as the central axis. It represents the radius of gyration of the helix, i.e. the outer radius of the gear hobbing cutter.

[0020] Preferably, the rotation matrix R x The calculation of is shown in formula (2):

[0021] (2)

[0022] Among them, θ(i) represents the rotation angle between the tool edge shape and the three-dimensional helical surface.

[0023] Preferably, the three-dimensional model of the gear hobbing cutter spiral is specifically shown in formula (3):

[0024] (3)

[0025] Among them, FX 1 (i, j), FY 1 (i, j), FZ 1 (i, j) represent the X-axis, Y-axis and Z-axis values ​​of the three-dimensional helical surface of the gear hobbing cutter respectively; r t 0 X(j),r t0 Y(j),r t 0 Z(j) represents the X-axis, Y-axis and Z-axis values ​​of the tool edge shape of the gear hobbing cutter respectively.

[0026] Preferably, in the step three, the method for obtaining the spatial curve of the tip of the rear row of teeth of the gear hobbing cutter is to transform the coordinates of the three-dimensional model of the gear hobbing cutter spiral and obtain it through interpolation processing. The specific method is: first, establish a spatial coordinate system with the central axis of the gear hobbing cutter as the X-axis, the center of the end face of the gear hobbing cutter as the origin, and the direction from the origin to the tip of the front row of teeth of the gear hobbing cutter as the Y-axis (the Z-axis direction can be set arbitrarily); define an angle with the rotation axis X-axis , and convert it to radians to generate a rotation matrix around the X axis , used to control the interception of the three-dimensional helical surface of the gear hobbing cutter, so as to obtain a section line with a certain angle to the X axis; and then define an angle with the Y axis , and convert it to radians to generate a rotation matrix around the Y axis , which is used to control the interception of the three-dimensional spiral surface of the gear hobbing cutter, so as to obtain a section line with a certain angle with the Y axis. , They correspond to the angles formed by the space curves of the rear row of gear hobbing cutter teeth and the front row of gear hobbing cutter teeth in the three-dimensional model of the gear hobbing cutter in the X-axis and Y-axis directions. and The calculation of is shown in the specific formula (4).

[0027] , (4)

[0028] Among them, m=1.

[0029] Next, all points on the three-dimensional helical surface of the gear hobbing cutter are transformed through the matrix , Rotate as shown in formula (5):

[0030] (5)

[0031] in, , , They respectively represent the X-axis, Y-axis and Z-axis values ​​of the three-dimensional helical surface of the rotating gear hobbing cutter.

[0032] Through this step, every point originally on the three-dimensional spiral surface of the gear hobbing cutter is rotated to a new position.

[0033] Preferably, at the rotated position, the intersection of the three-dimensional helical surface of the rotating gear hobbing cutter and the z=0 plane is calculated. For the points located on both sides of the plane z=0, according to each pair of adjacent points ( , ) to calculate the interpolation coefficients, and then calculate the intersection point by linear interpolation. The calculation of is shown in formula (6):

[0034] (6)

[0035] The calculation of the X and Y coordinates of the intersection point is shown in formula (7):

[0036] (7)

[0037] in, , , They represent the X-axis, Y-axis and Z-axis values ​​of the section obtained by linear interpolation respectively; K is the back-shoveling amount. When it is 0, it means no back-shoveling, corresponding to the spatial curve of the rear row of teeth without back-shoveling; when K is not 0, it corresponds to the spatial curve of the rear row of teeth after the back-shoveling.

[0038] Preferably, after finding the intersection, use the rotation matrix , The inverse matrix (i.e., the transposed matrix R 10 1 ′、R 20 2 ′), and restore these intersection points to the original coordinate system, as shown in formula (8):

[0039] (8)

[0040] in, , , They respectively represent the X-axis, Y-axis and Z-axis values ​​of the spatial curve of the tip of the rear row of gear hobbing cutters in the original coordinate system.

[0041] Preferably, based on formula (8), the previously calculated intersection point is restored from the rotated coordinate system to the original coordinate system, so that the oblique section of the three-dimensional spiral surface of the gear hobbing cutter can be obtained, that is, the spatial curve of the tip of the rear row of teeth of the gear hobbing cutter, specifically including the spatial curve of the rear row of teeth before back-cutting (K=0) and the spatial curve of the rear row of teeth after back-cutting (K≠0).

[0042] Preferably, in step 4, the Archimedean spiral in three-dimensional space is defined by independent parameters a, b and c, which respectively control the changes of the Archimedean spiral in different directions. Specifically:

[0043] Parameter a: controls the displacement rate in the X direction (linear growth along the screw axis).

[0044] Parameter b: controls the radial expansion rate of the spiral in plane YZ (i.e. the rate at which the radius changes with the angle).

[0045] Parameter c: controls the rate at which the spiral rises, that is, the rate at which the spiral changes in a linear direction (usually the Z axis or the X axis).

[0046] The radius and angle of the Archimedean spiral in polar coordinates are calculated by the space curve of the front row of blade tips and the space curve behind the rear row of blade shovels, as shown in formula (9):

[0047] , (9)

[0048] Among them, y1 and z1 are the Y-axis and Z-axis values ​​of the space curve coordinates of the front tooth tip, y2 and z2 are the Y-axis and Z-axis values ​​of the space curve coordinates behind the rear tooth shovel, r1 and r2 are the radii of the space curve coordinate points of the front tooth tip and the space curve coordinate points behind the rear tooth shovel in polar coordinates, respectively. and They respectively represent the angles in polar coordinates of the space curve coordinate point at the tip of the front row of teeth and the space curve coordinate point behind the rear row of teeth shovel.

[0049] Next, the angle change Δθ and radius change Δr between the corresponding two points in the space curve of the front row of cutter teeth tip and the space curve behind the rear row of cutter teeth shovel are calculated, as shown in formula (10):

[0050] (10)

[0051] Preferably, the Archimedean spiral parameters can be calculated using formulas (11), (12), and (13):

[0052] Parameter c: represents the rising speed of the spiral.

[0053] (11)

[0054] From the above formula, we can inversely calculate the parameters b and a of the Archimedean spiral:

[0055] Parameter b: represents the rate at which the spiral radius changes with the angle

[0056] (12)

[0057] Parameter a: represents the rate of change of the spiral segment with the angle in the x direction

[0058] (13)

[0059] Among them, x1 is the X-axis value of the spatial curve coordinate of the front row of cutter teeth, and x2 is the X-axis value of the spatial curve coordinate behind the rear row of cutter teeth.

[0060] Preferably, according to the inversely calculated parameters a, b and c, an Archimedean spiral segment passing through these two points (i.e., two corresponding points in the space curve of the front row of cutter teeth tip and the space curve behind the back row of cutter teeth) can be generated. Repeating the above steps for all discrete points constituting the space curve of the front row of cutter teeth tip and the space curve behind the back row of cutter teeth can obtain the Archimedean spiral cluster of the back face of the gear hobbing cutter under a given back relief amount.

[0061] The polar coordinate equation of the Archimedean spiral cluster can be calculated from formula (14):

[0062] (14)

[0063] in, is the rotation angle of the Archimedean spiral.

[0064] Preferably, the obtained Archimedean spiral cluster is converted into a Cartesian coordinate system to obtain the Archimedean spiral cluster l of the back face of the gear hobbing cutter under a given backing amount. AS (x3,y3,z3).

[0065] The x3, y3 and z3 coordinates of the Archimedean spiral cluster on the back face of the gear hobbing cutter under the given back relief amount are specifically shown in formula (15):

[0066] (15)

[0067] Preferably, in step five, the end space curve of the back face of the front row of teeth of the gear hobbing cutter is obtained by coordinate transformation and interpolation processing of the Archimedean spiral cluster on the back face of the gear hobbing cutter, so as to obtain the grinding wheel exit position of the front row of teeth in the final stage of back grinding, and the specific method is:

[0068] Substituting the Archimedean spiral cluster of the gear hobbing cutter back surface into formulas (4)-(8) for coordinate transformation and interpolation, the space curve r at the end of the gear hobbing cutter back surface of the front row of teeth can be obtained: t 1 (x4,y4,z4). The difference is that the value of m in formulas (4)-(8) is 2. and The rotation matrix is ​​obtained by corresponding to the angles formed by the space curve at the end of the back face of the front row of gear hobbing cutter and the space curve at the tip of the front row of gear hobbing cutter on the Archimedean spiral cluster on the back face of the gear hobbing cutter in the X-axis and Y-axis directions. , Then, the Archimedean spiral cluster (FX 2 (i, j), FY 2 (i, j), FZ 2 All points on the (i, j) (i.e., the x3, y3, and z3 coordinates of the Archimedean spiral cluster on the back face of the gear hobbing cutter obtained by formula (15)) are obtained through the matrix , The rotation is performed as shown in formula (5). Next, the intersection of the Archimedean spiral cluster on the back face of the gear hobbing cutter after rotation and the z=0 plane is calculated as shown in formulas (6) and (7), where K is 0. Finally, the rotation matrix , The inverse matrix R 10 2 ′、R 20 2 ′, and restore these intersection points to the original coordinate system to obtain the space curve of the end of the back face of the front row of teeth of the gear hobbing cutter.

[0069] Preferably, in step six, based on the end position (x4, y4, z4) of the flank face of the front row of gear hobbing cutter teeth and any point (x3, y3, z3) on the Archimedean spiral cluster on the flank face of the gear hobbing cutter, the intersection normal vector of the Archimedean spiral at the end position of the flank face of the front row of gear hobbing cutter teeth is calculated, as shown in formula (16):

[0070] (16)

[0071] The beneficial effects of the present invention are:

[0072] The method of the invention can accurately calculate the relationship between the gear hobbing cutter and the grinding wheel by establishing a three-dimensional model of the gear hobbing cutter spiral and obtaining the Archimedean spiral cluster on the back face of the gear hobbing cutter, thereby ensuring the accuracy of the calculation of the grinding wheel diameter.

[0073] In the process of establishing the three-dimensional spiral model of the gear hobbing cutter, the present invention accurately obtains the spatial curve of each tooth of the gear hobbing cutter by performing rotation interpolation processing on the spatial spiral line, thereby ensuring the calculation accuracy; in the process of calculating the Archimedean spiral cluster of the gear hobbing cutter back face, the actual configuration of the Archimedean spiral constituting the gear hobbing cutter back face is obtained through inverse operation, and the interpolation processing is performed on it and the intersection normal vector is obtained, thereby ensuring that the spatial position of the grinding wheel corresponds accurately to the actual processing process.

[0074] A gear hobbing cutter grinding wheel diameter calculation device based on the Archimedean spiral relationship constructed based on the method of the present invention can automatically process and analyze data, thereby being able to quickly calculate the grinding wheel diameter, reduce human calculation errors, and improve the efficiency of processing design. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 The present invention is a flow chart of a method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship.

[0076] Figure 2 The tool edge shape of the gear hobbing cutter is shown.

[0077] Figure 3 It is the groove between two teeth of the gear hobbing cutter.

[0078] Figure 4 The positional relationship between the gear hobbing cutter tooth grooves and the front and rear rows of gear hobbing cutter teeth is shown.

[0079] Figure 5 The simulation results of the gear hobbing cutter and the grinding wheel are given.

[0080] Figure 6 is a graphic representation of the calculation results of the grinding wheel diameter.

[0081] Figure 7 Create an APP operation example. DETAILED DESCRIPTION

[0082] like Figure 1 A method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship of the present invention comprises the following steps:

[0083] First, input the basic geometric parameters and processing parameters of the gear hobbing cutter. These parameters define the shape, size and cutting conditions of the gear hobbing cutter. They mainly include the following:

[0084] Gear hobbing cutter outer radius r g : Defined as 20 mm.

[0085] Gear hobbing cutter relief amount K: defined as 1.5 mm, used to indicate the relief amount of the hob back face.

[0086] Gear hobbing cutter helix angle β: Define the gear hobbing cutter helix angle as 3°1′ and convert it into radians for subsequent calculations.

[0087] Number of chip grooves N: Defined as 12, used to define the number of teeth of the gear hobbing cutter.

[0088] Chip groove direction: If a straight groove design is adopted, the chip groove lead L is 0.

[0089] Grinding length l: defined as 3.8 mm.

[0090] Tooth height h: defined as 4.45 mm.

[0091] Slot width w: defined as 4 mm.

[0092] Tool edge shape of gear hobbing cutter: Figure 2The tool blade shape of the gear hobbing cutter is specifically composed of two-dimensional blade shape data points read by mathematical modeling software; the middle position of the blade shape is intercepted, that is, Figure 3 The cutter groove between two teeth of the gear hobbing cutter shown is used as the main tool edge shape for discussion and calculation.

[0093] Construct a three-dimensional model of the gear hobbing cutter spiral. Use formulas (1), (2), and (3) to establish Figure 5 The three-dimensional spiral surface of the gear hobbing cutter is shown in Figure 1, and the following Figure 4 The spiral surface F(FX 1 , FY 1 , FZ 1 ).

[0094] The space curve of the tip of the rear row of teeth and the space curve of the tip of the front row of teeth are obtained. The space curve of the tip of the rear row of teeth includes the space curve of the back of the rear row of teeth and the space curve of the back of the rear row of teeth. t 0 Specifically, it is based on the tool blade shape of the gear hobbing cutter and is obtained according to mathematical modeling software. The calculation method of the space curve of the rear row of cutter teeth before back-cutting is the same as the space curve of the rear row of cutter teeth after back-cutting. Formulas (4), (5), (6), (7), and (8) are directly used to obtain the cross-section of the spiral surface F at different positions, such as Figure 4 As shown. Among them, r0 2 is the angle between the helicoid F and the rotation axis X =360° / N position, since the chip groove is a straight groove, the lead angle Set to 0°, if the chip groove is designed as an inclined groove, the lead angle, that is, the angle with the Y axis The calculation formula is For the calculation of the space curve behind the rear row of cutter teeth, note that after performing formulas (4), (5), (6), and (7), that is, after obtaining the section between the deflected helical surface F and the Z=0 plane, the section is processed by subtracting the K value from the Y coordinate, that is, the back processing, and then the section is transformed back to the original helical surface position (that is, the original coordinate system) through formula (8) to obtain the section r t 2 .like Figure 4 As shown, this operation can ensure that r0 2 With r t 2 It is parallel in the radial direction of the spiral surface F, which is consistent with the operation of scraping the back of the back of the tool surface during the process of grinding the gear hobbing cutter with the grinding wheel.

[0095] The curve r obtained at this time t 0 is the space curve of the front row of teeth tip, r0 2is the spatial curve of the rear teeth without back-cutting, i.e. the cutting edge of the rear teeth of the gear hobbing cutter, r t 2 It is the spatial curve behind the rear row of blade teeth at a given backhoe length.

[0096] Calculate the Archimedean spiral cluster on the back face of the gear hobbing cutter. By using formulas (9), (10), (11), (12), (13), (14), and (15), we can inversely calculate Figure 4 The Archimedean spiral cluster l AS These curves constitute the back surface of the gear hobbing cutter behind the shovel.

[0097] Archimedean spiral cluster on the back face of gear hobbing cutter AS The tangent line of the spiral cluster at the grinding length l of the back cutting edge is obtained by formulas (4), (5), (6), (7), and (8), that is, the spatial curve r at the end of the back cutting edge of the front row of gear hobbing cutters: t 1 ,like Figure 4 As shown, at this time , Depends on the chip flute lead.

[0098] Because the normal vector of the machined surface must pass through the center of rotation of the tool at the moment of machining during the machining process, the Archimedean spiral cluster l AS The intersection normal vector at the end position of the back face of the front row of teeth of the gear hobbing cutter (back face grinding length l) is obtained by using formula (16) and extended.

[0099] When the hobbing cutter back face is relieved and ground, the front row of teeth are prone to interference with the back row of teeth at the final stage of machining, that is, at the end of the space curve r of the back face of the front row of teeth of the hobbing cutter t 1 (abbreviated as intercept r t 1 ) position is easy to be with the space curve r0 of the rear row of cutter teeth without back-cutting 2 (abbreviated as intercept r0 2 ) interference, the maximum grinding wheel diameter without interference is the diameter of the grinding wheel when interference occurs. t 1 , Intercept r0 2 They are all composed of discrete points in space, and it is known that the center of the grinding wheel is on the intersection normal vector n. So we can find the intercept r t 1 , Intercept r0 2 The median perpendicular plane p between them is calculated, and the intersection point of the intersection normal vector n and the median perpendicular plane p in three-dimensional space can be obtained to obtain the center position of the grinding wheel, and the intersection line r of the center on the intersection normal vector n can be obtained. t 1, Intercept r0 2 The maximum circumscribed circle of the corresponding points in space.

[0100] Calculate the center position of each circle and the intersection r t 1 The distance between each point can be used to obtain the radius of the grinding wheel at this time, which can be converted into diameter and output as follows: Figure 6 The calculation result is that the minimum value is the maximum grinding wheel diameter that meets the requirements without interference. The calculation result is 44.0858 mm.

[0101] An embodiment of the present invention further provides a device for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship, the device comprising:

[0102] The parameter setting module is used to set the geometric parameters of the gear hobbing cutter, including the outer diameter of the gear hobbing cutter, grinding length, back relief, helix angle, number of chip grooves, tool edge shape, and chip groove lead;

[0103] A gear hobbing cutter spiral 3D model building module is used to generate a gear hobbing cutter spiral line according to given gear hobbing cutter geometric parameters, and to combine the gear hobbing cutter spiral line with the tool edge shape of the gear hobbing cutter through translation and rotation to generate a gear hobbing cutter spiral 3D model;

[0104] A module for constructing a space curve of the tip of the rear row of teeth and the tip of the front row of teeth of a gear hobbing cutter is used to perform coordinate transformation and interpolation processing on a three-dimensional spiral model of the gear hobbing cutter to extract the space curve of the tip of the rear row of teeth of the gear hobbing cutter, wherein the space curve of the tip of the rear row of teeth of the gear hobbing cutter includes a space curve of the back of the rear row of teeth and a space curve of the back of the rear row of teeth without being scraped back; based on the tool shape of the gear hobbing cutter, the space curve of the tip of the front row of teeth is obtained according to mathematical modeling software;

[0105] A module for calculating Archimedean spiral clusters on the flank of a gear hobbing cutter, for calculating Archimedean spiral clusters on the flank of a gear hobbing cutter under a given backing amount according to the space curve of the front row of cutter teeth tips and the space curve of the backing of the rear row of cutter teeth;

[0106] A module for constructing a space curve at the end of the back face of the front row of gear hobbing cutters is used to perform coordinate transformation and interpolation processing on the Archimedean spiral cluster on the back face of the gear hobbing cutters to obtain a space curve at the end of the back face of the front row of gear hobbing cutters;

[0107] An intersection normal vector calculation module is used to obtain the intersection normal vector of the Archimedean spiral at the end of the flank face of the front row of gear hobbing cutter based on the space curve at the end of the flank face of the front row of gear hobbing cutter and the Archimedean spiral cluster on the flank face of the gear hobbing cutter;

[0108] The maximum diameter calculation module of the grinding wheel is used to calculate the perpendicular surface between the spatial curve of the end of the back face of the front row of teeth of the gear hobbing cutter and the spatial curve of the back row of teeth without back-removing according to the intersection normal vector, the spatial curve of the end of the back face of the front row of teeth of the gear hobbing cutter, and the spatial curve of the back row of teeth without back-removing. The final center position of the grinding wheel is obtained by calculating the intersection point of the intersection normal vector and the perpendicular surface. The minimum distance between the center and the end of the back face of the front row of teeth of the gear hobbing cutter is the maximum diameter of the grinding wheel without interference.

[0109] An embodiment of the present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship.

[0110] An embodiment of the present invention further provides a computer-readable storage medium having computer instructions stored thereon, wherein the computer instructions are used to enable a computer to execute the steps of the one or more processors to implement the method for calculating the diameter of a gear hobbing cutter grinding wheel based on an Archimedean spiral relationship.

[0111] Based on the method of the present invention, an APP for calculating the diameter of a gear hobbing cutter grinding wheel can be developed. By using the powerful calculation and simulation functions of mathematical modeling software, the shortcomings of traditional methods can be overcome, and the accuracy of grinding wheel processing gear hobbing cutters can be significantly improved, and the development time of grinding wheel products can be reduced. In order to facilitate enterprise production and make this method more practical, the tool edge shape r of the gear hobbing cutter that needs to be read is replaced by the tool tooth height h and the tool groove width w through a simplified model. t 0 , making APP convenient and efficient. Figure 7 The calculation result of the APP shown is 43.7075, with an error of 0.86% which is within the allowable range.

Claims

1. A method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship, which is used to accurately determine the maximum diameter of the grinding wheel used in the process of machining a gear hobbing cutter; characterized in that: The method comprises the following steps: Step 1: Given the geometric parameters of the gear hobbing cutter, including the outer diameter of the gear hobbing cutter, grinding length, back relief, helix angle, number of chip grooves, tool edge shape, and chip groove lead; Step 2: Construct a three-dimensional model of the gear hobbing cutter spiral, specifically: Firstly, the gear hobbing cutter helix is ​​generated according to the given gear hobbing cutter geometric parameters; Then, the gear hobbing cutter spiral line and the gear hobbing cutter tool edge shape are combined through translation and rotation to generate a gear hobbing cutter spiral three-dimensional model; Step 3: Obtaining the space curve of the tip of the rear row of teeth and the space curve of the tip of the front row of teeth of the gear hobbing cutter, specifically: performing coordinate transformation and interpolation processing on the spiral three-dimensional model of the gear hobbing cutter to extract the space curve of the tip of the rear row of teeth of the gear hobbing cutter, wherein the space curve of the tip of the rear row of teeth of the gear hobbing cutter includes the space curve of the back of the rear row of teeth and the space curve of the back of the rear row of teeth; based on the tool blade shape of the gear hobbing cutter, the space curve of the tip of the front row of teeth is obtained according to the mathematical modeling software; Step 4: Calculate the Archimedean spiral clusters on the flank of the gear hobbing cutter, specifically: calculate the Archimedean spiral clusters on the flank of the gear hobbing cutter under a given backing amount according to the space curve of the front row of cutter teeth tips and the space curve of the backing of the rear row of cutter teeth; Step 5: coordinate transformation and interpolation processing are performed on the Archimedean spiral cluster of the gear hobbing cutter flank to obtain the end space curve of the flank of the front row of teeth of the gear hobbing cutter; Step 6: based on the space curve of the end of the flank surface of the front row of gear hobbing cutter teeth and the Archimedean spiral cluster of the flank surface of the gear hobbing cutter, obtain the intersection normal vector of the Archimedean spiral at the end of the flank surface of the front row of gear hobbing cutter teeth; Step 7: Calculate the maximum diameter of the grinding wheel. The specific method is: calculate the perpendicular surface between the spatial curve of the end of the back face of the front row of gear hobbing teeth and the spatial curve of the back row of gear hobbing teeth without back-shoveling according to the intersection normal vector, the spatial curve of the end of the back face of the front row of gear hobbing teeth and the spatial curve of the back row of gear hobbing teeth without back-shoveling, and obtain the final center position of the grinding wheel by calculating the intersection of the intersection normal vector and the perpendicular surface. The minimum distance between the center and the end of the back face of the front row of gear hobbing teeth is the maximum diameter of the grinding wheel without interference. In step 2, the calculation of the gear hobbing cutter helix l1 is shown in formula (1): Among them, (l1X i ,l1Y i ,l1Z i ) represents the coordinates of the helix of the gear hobbing cutter, x(i) represents the X-axis value corresponding to point i on the curve obtained by the linear uniform growth of the helix with the X-axis as the central axis, r g Indicates the radius of gyration of the helix, i.e. the outer radius of the gear hobbing cutter; In step 2, the gear hobbing cutter spiral line and the gear hobbing cutter tool edge shape are combined by translation and rotation to generate a gear hobbing cutter spiral three-dimensional model. The specific method is to use the rotation matrix R x The tool edge shape of the gear hobbing cutter is r t 0 Rotate and translate to the three-dimensional spiral surface of the gear hobbing cutter under given geometric parameters, so as to obtain the three-dimensional spiral model of the gear hobbing cutter; Rotation matrix R x The calculation of is shown in formula (2): Among them, θ(i) represents the rotation angle between the tool edge shape and the three-dimensional helical surface; The three-dimensional model of the gear hobbing cutter spiral is specifically shown in formula (3): Among them, FX 1 (i, j), FY 1 (i, j), FZ 1 (i, j) represent the X-axis, Y-axis and Z-axis values ​​of the three-dimensional helical surface of the gear hobbing cutter respectively; r t 0 X(j), r t 0 Y(j), r t 0 Z(j) represents the X-axis, Y-axis and Z-axis values ​​of the tool edge shape of the gear hobbing cutter.

2. The method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship according to claim 1, characterized in that: In step 3, coordinate transformation and interpolation processing are performed on the three-dimensional model of the gear hobbing cutter spiral to extract the space curve of the tip of the rear row of gear hobbing cutter teeth, and in step 5, coordinate transformation and interpolation processing are performed on the Archimedean spiral cluster of the gear hobbing cutter back surface to obtain the space curve of the end of the back surface of the front row of gear hobbing cutter teeth; wherein, the coordinate transformation and interpolation processing are specifically as follows: First, establish a spatial coordinate system with the central axis of the gear hobbing cutter as the X-axis, the center of the end face of the gear hobbing cutter as the origin, and the point from the origin to the tip of the front row of gear hobbing cutters as the Y-axis, in which the Z-axis is set arbitrarily; Then, define an angle α0 with the X axis m , and convert it to radians to generate the rotation matrix R around the X axis 10 m ; Define an angle β0 with the Y axis m , and convert it to radians to generate the rotation matrix R around the Y axis 20 m ; When m = 1, α0 1 , β0 1 They correspond to the angles formed by the space curves of the rear row of gear cutting teeth and the front row of gear cutting teeth in the three-dimensional model of the gear cutting cutter in the X-axis and Y-axis directions; when m = 2, α0 2 , β0 2 The rotation matrix R corresponds to the angles formed by the space curve at the end of the back face of the front row of gear hobbing cutter and the space curve at the tip of the front row of gear hobbing cutter on the Archimedean spiral cluster on the back face of the gear hobbing cutter in the X-axis and Y-axis directions. 10 m and R 20 m The calculation of is shown in the specific formula (4): Next, the three-dimensional helical surface (FX 1 (i, j), FY 1 (i, j), FZ 1 (i, j)) or Archimedean spiral cluster on the back face of the gear hobbing cutter (FX 2 (i, j), FY 2 (i, j), FZ 2 All points on (i, j)) are passed through the matrix Rotate as shown in formula (5): Among them, Fr0X m (i,j), Fr0Y m (i,j), Fr0Z m (i, j) represent the X-axis, Y-axis and Z-axis values ​​of the three-dimensional helical surface of the rotating gear hobbing cutter or the Archimedean spiral cluster on the back face of the gear hobbing cutter, respectively, corresponding to m=1 or 2; At the rotated position, calculate the intersection of the three-dimensional helical surface of the rotating gear hobbing cutter or the Archimedean spiral cluster of the gear hobbing cutter back face with the z = 0 plane, corresponding to m = 1 or 2 respectively; for the points on both sides of the plane z = 0, according to each pair of adjacent points (Fr0Z m (i,j),Fr0Z m (i+1,j+1)) to calculate the interpolation coefficient, and then calculate the intersection point by linear interpolation; where the interpolation coefficient t m The calculation of is shown in formula (6): The calculation of the coordinates of the intersection point is specifically shown in formula (7): Among them, Pi0X m (i),Pi0Y m (i),Pi0Z m (i) respectively represent the X-axis, Y-axis and Z-axis values ​​of the section obtained by linear interpolation; K is the back-cutting amount, when it is 0, it means no back-cutting, corresponding to the space curve of the rear row of cutter teeth without back-cutting or the space curve of the end of the back face of the front row of cutter teeth of the gear hobbing cutter, corresponding to m=1 or 2 respectively; when K is not 0, it corresponds to the space curve of the back face of the rear row of cutter teeth, corresponding to m=1; After finding the intersection point, use the rotation matrix R 10 m , R 20 m The inverse matrix R 10 m ′、R 20 m ′, restore these intersection points to the original coordinate system, as shown in formula (8): Among them, Prb0X m (i), Prb0Y m (i), Prb0Z m (i) respectively represent the X-axis, Y-axis and Z-axis values ​​of the spatial curve of the tip of the rear row of gear hobbing teeth or the spatial curve of the end of the back face of the front row of gear hobbing teeth in the original coordinate system, corresponding to m=1 or 2 respectively.

3. The method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship according to claim 2, characterized in that: The step 4 specifically comprises the following steps: First, the radius and angle of the Archimedean spiral in polar coordinates are calculated through the space curve of the front row of cutter teeth and the space curve behind the rear row of cutter teeth, as shown in formula (9): Among them, y1 and z1 are the Y-axis and Z-axis values ​​of the space curve coordinates of the front tooth tip, y2 and z2 are the Y-axis and Z-axis values ​​of the space curve coordinates behind the rear tooth shovel, r1 and r2 represent the radii of the space curve coordinate points of the front tooth tip and the space curve coordinate points behind the rear tooth shovel in polar coordinates, θ1 and θ2 represent the angles of the space curve coordinate points of the front tooth tip and the space curve coordinate points behind the rear tooth shovel in polar coordinates; Next, the angle change Δθ and radius change Δr between the corresponding two points in the space curve of the front tooth tip and the space curve behind the rear tooth shovel are calculated, as shown in formula (10): Then, calculate the Archimedean spiral parameters a, b and c: Parameter c: represents the rising speed of the spiral: Parameter b: represents the rate at which the spiral radius changes with the angle: Parameter a: represents the rate of change of the spiral segment with the angle in the x direction: Among them, x1 is the X-axis value of the spatial curve coordinate of the front row of cutter teeth, and x2 is the X-axis value of the spatial curve coordinate behind the rear row of cutter teeth. According to the parameters a, b and c, an Archimedean spiral segment passing through two corresponding points in the space curve of the front tooth tip and the space curve behind the back tooth shovel is generated; the above steps are repeated for all the discrete points constituting the space curve of the front tooth tip and the space curve behind the back tooth shovel to obtain the Archimedean spiral cluster of the back face of the gear hobbing cutter under a given back face amount; The polar coordinate equation of the Archimedean spiral cluster is calculated by formula (14): r(θ)=r1+b(θ-θ1) (14) Where θ is the rotation angle of the Archimedean spiral; The obtained Archimedean spiral cluster is converted into the Cartesian coordinate system to obtain the Archimedean spiral cluster l on the back face of the gear hobbing cutter under a given back relief amount. AS (x3, y3, z3); ​​the x3, y3 and z3 coordinates of the Archimedean spiral cluster on the back face of the gear hobbing cutter under the given back relief amount are specifically shown in formula (15):

4. The method for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship according to claim 1, characterized in that: Specifically, step 6 is to calculate the intersection normal vector of the Archimedean spiral at the end position of the flank face of the front row of gear hobbing cutter teeth based on the end position (x4, y4, z4) of the flank face of the front row of gear hobbing cutter teeth and any point (x3, y3, z3) on the Archimedean spiral cluster on the flank face of the gear hobbing cutter, as shown in formula (16): Where n is the intersection normal vector.

5. A device for calculating the diameter of a gear hobbing cutter grinding wheel based on the Archimedean spiral relationship, using the method according to any one of claims 1 to 4, characterized in that: include: The parameter setting module is used to set the geometric parameters of the gear hobbing cutter, including the outer diameter of the gear hobbing cutter, grinding length, back relief, helix angle, number of chip grooves, tool edge shape, and chip groove lead; A gear hobbing cutter spiral 3D model building module is used to generate a gear hobbing cutter spiral line according to given gear hobbing cutter geometric parameters, and to combine the gear hobbing cutter spiral line with the tool edge shape of the gear hobbing cutter through translation and rotation to generate a gear hobbing cutter spiral 3D model; A module for constructing a space curve of the tip of the rear row of teeth and the tip of the front row of teeth of a gear hobbing cutter is used to perform coordinate transformation and interpolation processing on a three-dimensional spiral model of the gear hobbing cutter to extract the space curve of the tip of the rear row of teeth of the gear hobbing cutter, wherein the space curve of the tip of the rear row of teeth of the gear hobbing cutter includes a space curve of the back of the rear row of teeth and a space curve of the back of the rear row of teeth without being scraped back; based on the tool shape of the gear hobbing cutter, the space curve of the tip of the front row of teeth is obtained according to mathematical modeling software; A module for calculating Archimedean spiral clusters on the flank of a gear hobbing cutter, for calculating Archimedean spiral clusters on the flank of a gear hobbing cutter under a given backing amount according to the space curve of the front row of cutter teeth tips and the space curve of the backing of the rear row of cutter teeth; A module for constructing a space curve at the end of the back face of the front row of gear hobbing cutters is used to perform coordinate transformation and interpolation processing on the Archimedean spiral cluster on the back face of the gear hobbing cutters to obtain a space curve at the end of the back face of the front row of gear hobbing cutters; An intersection normal vector calculation module is used to obtain the intersection normal vector of the Archimedean spiral at the end of the flank face of the front row of gear hobbing cutter based on the space curve at the end of the flank face of the front row of gear hobbing cutter and the Archimedean spiral cluster on the flank face of the gear hobbing cutter; The maximum diameter calculation module of the grinding wheel is used to calculate the perpendicular surface between the spatial curve of the end of the back face of the front row of teeth of the gear hobbing cutter and the spatial curve of the back row of teeth without back-removing according to the intersection normal vector, the spatial curve of the end of the back face of the front row of teeth of the gear hobbing cutter, and the spatial curve of the back row of teeth without back-removing. The final center position of the grinding wheel is obtained by calculating the intersection point of the intersection normal vector and the perpendicular surface. The minimum distance between the center and the end of the back face of the front row of teeth of the gear hobbing cutter is the maximum diameter of the grinding wheel without interference.

6. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having computer instructions stored thereon, characterized in that: The computer instructions are used to enable a computer to execute the steps of the method according to any one of claims 1 to 4.

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