Parametric design method of milling cutter with tangent circular arc end surface generatrix

Abstract

The application discloses a kind of end rotary surface generatrix parameterization design method of tangent circular arc of milling cutter, comprising: defining tool parameters, constructing coordinate system and tool end rotary surface parameterization structure model, according to the calculation formula of the geometric relationship between tool parameters, the circular arc of ring part generatrix and bottom generatrix circular arc are expressed as expression, the geometric relationship of tool parameters is analyzed, and the parameterization of tool design is realized.The milling cutter of the application can improve the machining quality compared with the ball end milling cutter, improve the tool life, reduce the production cost;The material removal rate of the ball end milling cutter with the same tool diameter is larger, and the machining efficiency is higher;The design parameters of the tool end rotary surface generatrix can be adjusted according to specific requirements, so that the tool can adapt to different machining tasks.This flexibility enables the tool to cope with different materials, sizes and geometric shapes of workpieces.Parameterized tool can be used for machining of different curvature surfaces, and the best tool parameter combination is selected.

Description

Technical Field

[0001] This invention relates to the field of end mill design technology, specifically to a parametric design method for end mills with a tangent circular arc as the generatrix of the end rotation surface. Background Technology

[0002] Currently, with the development of the mold manufacturing industry, the demand for milling cutters for mold finishing is constantly increasing. Currently, mold finishing processes are mostly completed using ball end mills and ring end mills. The end face of a ball end mill is spherical, and the selection of the ball end radius needs to be considered during design. An excessively large ball end radius may reduce machining quality, while an excessively small ball end radius may limit tool strength, machining efficiency, and tool life. Ring end mills, due to the limitations of their end shape, are not suitable for finishing complex curved surfaces, and may be unable to reduce residual height due to tool limitations, thus affecting machining accuracy and surface quality. Summary of the Invention

[0003] The purpose of this invention is to provide a parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end rotation surface, in order to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end revolution surface, comprising the following steps:

[0005] Step 1: Define the tool radius, that is, the radius of the tool holder is R;

[0006] Define the radius of the arc of the generatrix of the annular torus as r1;

[0007] Define the radius of the arc of the generatrix of the bottom sphere as r2; r2 > R;

[0008] Define the central angle of the generatrix arc of the toroidal surface as θ1;

[0009] Define the central angle of the generatrix of the bottom sphere as θ2;

[0010] Step 2: Construct a parametric structural model of the coordinate system and the tool end face of revolution;

[0011] With the center of the intersection of the perimeter and the ring as the origin O of the coordinate system m Establish the tool's rectangular coordinate system O m -XYZ, with the tool's rotation axis as the Z-axis, the endpoint of the bottom spherical generatrix as the tool tip, and the vertical upward direction along the tool tip as the Z-axis direction. The starting position of the peripheral cutting edge is the X-axis direction, and the Y-axis direction follows the right-hand rule, limiting O. e On the Z-axis, O r On the X-axis;

[0012] In the XOZ plane, with the point (R-r1, 0) as the center, r1 as the radius, and θ1 as the central angle, 0 ≤ θ1 ≤ 90°, construct the annular generatrix arc Arc starting from (R, 0). r With point (0, (R-r1)cotθ1) as the center, (R-r1)secθ1+r1 as the radius, and θ2 as the central angle, θ1+θ2=π / 2, construct the bottom generatrix arc Arc starting from (R-r1+r1 cosθ1, -r1 sinθ1). e ;

[0013] Step 3: Construct calculation formulas for tool parameters based on geometric relationships;

[0014] Let point A be (R-r1+r1 cosθ1, -r1 sinθ1), and let r2 = (R-r1)secθ1+r1. Then the axial length of the tool tip D = r2-O e O m D = r2 - (r2 - r1)sinθ1; D is less than R;

[0015] Step 4: Express the circular arc of the ring and the circular arc of the bottom generatrix as expressions for R, D, and θ1;

[0016] The radius r1 of the annular arc generatrix and the radius r2 of the bottom spherical arc generatrix are obtained from the calculation formula in step three.

[0017] Furthermore, in step four, the radius r1 of the annular arc generatrix and the radius r2 of the bottom spherical arc generatrix rotate around the Z-axis to form the annular torus S. r and the bottom spherical S e The annular surface S of the ring portion r and the bottom spherical S e The calculation formula is

[0018] Where θ is a surface parameter, which is the angle between the radial line at any point on the tool surface and the Z-axis; For surface parameters, X is the angle between the radial line at any point on the tool surface and the XOZ plane. r Y r Z r For the annular surface S r The coordinates of any point on the x-axis, X e Y e Z e For the bottom spherical surface S e The coordinates of any point on the [above].

[0019] Furthermore, in step two, the arc of the ring-shaped generatrix... rand bottom arc generatrix Arc e The calculation formula is

[0020] Where x r , z r Arc of the ring-shaped generatrix r The coordinates of any point on the x-axis, e , z e Arc of the bottom generatrix r The coordinates of any point on the [above].

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] (1) By analyzing the geometric relationship of tool parameters, the parameterization of tool design is effectively realized. Tools designed in this way can improve machining efficiency, improve machining quality, increase tool life and reduce production costs; the material removal rate of the tool is greater and the machining efficiency is higher under the same tool diameter.

[0023] (2) Parametric design of the tool tip rotation surface can adjust the design parameters according to specific needs, making the tool adaptable to different machining tasks. This flexibility enables the tool to handle workpieces of different materials, sizes and geometries. Parametric tools can machine surfaces with different curvatures and select the best combination of tool parameters. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the structure of the cutting tool of the present invention;

[0025] Figure 2 This is a schematic diagram of the generatrix of the rotating surface of the cutting tool of the present invention;

[0026] Figure 3 This is a schematic diagram illustrating the solution for the circular arc radius r1 of the ring portion and the circular arc radius r2 of the bottom spherical surface of the cutting tool of the present invention;

[0027] Figure 4 This is a schematic diagram of the tool's rotation surface according to the present invention;

[0028] Figure 5 This is a curve diagram of the longitudinal section profile of the tool of the present invention.

[0029] In the diagram: 1. Peripheral cylindrical surface; 2. Ring-shaped toroidal surface; 3. Bottom spherical surface; 4. Cutting tool. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Example:

[0032] Please see Figure 1-5 The present invention provides a technical solution: a parametric design method for a milling cutter with a tangent circular arc as the generatrix of the end rotation surface;

[0033] The design focuses on the generatrix radius r1 of the annular surface 2 and the generatrix radius r2 of the bottom spherical surface 3 of the tool 4. The technical solution implemented is as follows:

[0034] Step 1: Define the geometric parameters of the tool's 4-plane of revolution:

[0035] Define the radius of the tool 4, that is, the radius of the tool holder, as R. In this implementation, R = 5mm.

[0036] Define the axial length of the cutting edge at the end of the tool as D, and in this implementation, D = 4mm;

[0037] Define the central angle of the generatrix arc of the torus as θ1, and in this implementation, take θ1 = 60°;

[0038] Step 2: Construct the coordinate system and parametric structural model of the tool's four end faces of revolution:

[0039] With the tool's 4-axis rotation as the Z-axis, the O-axis is defined. e On the Z-axis, O r On the X-axis, the central angle of the generatrix of the annular revolution surface is θ1, and the central angle of the generatrix of the bottom spherical surface 3 is θ2. θ2 and θ1 satisfy the formula θ1+θ2=π / 2.

[0040] With the center of the intersection of circumference 1 and ring 2 as the origin O of the coordinate system m Establish the tool's rectangular coordinate system O m -XYZ, with the tool's rotation axis as the Z-axis, the endpoint of the bottom spherical generatrix as the tool tip, and the vertical upward direction along the tool tip as the Z-axis direction. The starting position of the peripheral cutting edge is the X-axis direction, and the Y-axis direction follows the right-hand rule, limiting O. e On the Z-axis, O r On the X-axis;

[0041] Let the radius of the arc of the generatrix of the torus be r1, and the radius of the arc of the generatrix of the bottom sphere be r2. In the XOZ plane, with the point (R-r1, 0) as the center, r1 as the radius, θ1 as the central angle, and (R, 0) as the starting point, construct the arc of the generatrix Arc of the torus. r With point (0, (R-r1)cotθ1) as the center, (R-r1)secθ1+r1 as the radius, θ2 as the central angle, and (R-r1+r1cosθ1, -r1sinθ1) as the starting point, construct the bottom generatrix arc Arc. e ;

[0042] Step 3: Construct the relationship between the four tool parameters based on geometric relationships:

[0043] Let (R-r1+r1 cosθ1, -r1 sinθ1) be point A, and let r2 = (R-r1)secθ1+r1. Then the axial length D of the end of the tool 4 is D = r2-O. e O m ,Right now

[0044] D=r2-(r2-r1)sinθ1 (1)

[0045] Step 4: Express the two arcs as expressions for R, D, and θ1:

[0046] From the geometric relationship in step three, the radius r1 of the generatrix of the annular arc and the radius r2 of the generatrix of the bottom spherical arc can be obtained, as follows:

[0047]

[0048]

[0049] Substituting R = 5mm, D = 4mm, and θ1 = 60° into the above formula, we can obtain r1 = 3.6mm and r2 = 6.4mm.

[0050] In this embodiment, combined with Figure 3 and Figure 4 This embodiment further defines the end-face rotation design method described in Specific Embodiment 1. This embodiment describes a parametric design method for a milling cutter where the generatrix of the end-face rotation is two tangent circular arcs. In step four, the two circular arcs with radii r1 and r2 rotate around the Z-axis to form a ring-shaped annular surface 2S. r and the bottom spherical 3S e .

[0051] In this embodiment, combined with Figure 3To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. In step 1, D < R, and the values taken here obviously meet the conditions.

[0052] In this embodiment, in combination with Figure 4 To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. In step 1, the radius r2 of the bottom spherical surface 3 > R. Through calculation, it can be seen that the values adopted in this embodiment meet the requirements.

[0053] In this embodiment, in combination with Figure 4 To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. In step 2, θ1 + θ2 = π / 2; here θ1 = 60°, θ2 = 30°.

[0054] In this embodiment, in combination with Figure 2 To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. The two arcs are smoothly tangent and connected.

[0055] In this embodiment, in combination with Figure 3 To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. In step 2, θ1, 0° ≤ θ1 ≤ 90°, where θ1 is the central angle of the circular arc of the generatrix of the toroidal surface.

[0056] In this embodiment, in combination with Figure 3 To describe this embodiment, this embodiment further limits the end surface rotation design method described in the first specific embodiment. A parameterized design method for a milling cutter with the generatrix of the end surface rotation being two tangent arcs. In step 2, the circular arc of the ring part generatrix is Arc r and the circular arc of the bottom generatrix is Arc e , and their expressions are as follows:

[0057] The circular arc of the bottom generatrix Arc e The expression is as follows:

[0058]

[0059] Arc of the ring section r The expression is as follows:

[0060]

[0061] In this embodiment, combined with Figure 3 This embodiment further defines the end-face rotation design method described in Specific Embodiment 1. This embodiment describes a parametric design method for a milling cutter where the generatrix of the end-face rotation is two tangent circular arcs. The annular surface 2 is S... r And the bottom spherical surface 3 is S e It can be expressed by the following formula;

[0062] Circular toroidal surface 2S r The expression is as follows:

[0063]

[0064] Bottom Spherical 3S e The expression is as follows:

[0065]

[0066] Combining the above formulas (1-7), we can obtain the relationship between r1, r2, θ1, R, and D, which is the parametric model of the end face of revolution. To achieve applicability for surface machining, the values ​​of r1 and r2 can be changed simply by adjusting the four tool parameters θ1, R, and D.

[0067] When different parameters are selected, the rotating surface of tool 4 can meet the machining of most curved surfaces. In the above specific implementation process, the radius R of tool 4 is selected as 5mm, the end cutting length D is 4mm, and the central angle θ1 of the generatrix of the toroidal surface is 60°.

[0068] By selecting different parameters to obtain the longitudinal section profile curve of tool 4, it can be seen that the parametric design method of tool 4 can process curved surfaces of various shapes, has strong applicability, and meets the design requirements.

[0069] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end revolution surface, characterized in that, Includes the following steps: Step 1: Define the tool radius, i.e., the radius of the tool holder. R ; Define the radius of the arc of the generatrix of the toroidal surface as: r 1; Define the radius of the arc of the generatrix of the bottom sphere as: r 2; Define the central angle of the generatrix arc of the toroidal surface as . θ 1; Define the central angle of the arc of the generatrix of the bottom sphere as θ 2; Step 2: Construct a parametric structural model of the coordinate system and the tool end face of revolution; The origin of the coordinate system is the center of the intersection of the perimeter and the ring. O m Establish a rectangular coordinate system for the tool. O m - XYZ With the tool rotation axis as Z The endpoint of the bottom spherical generatrix arc is the tool tip point. The Z-axis direction is perpendicularly upward from the tool tip point, with the direction of the starting position of the peripheral cutting edge as the axis. X Axial direction, Y The axial direction follows the right-hand rule, which limits... O e exist Z On the axis, O r exist X On the axis; exist XOZ Within the plane, with points ( R - r With 1, 0 as the center, and r With a radius of 1, θ 1 is the central angle, with ( R Starting from 0, construct the generatrix arc of the annular torus. Arc r , with point (0, ( R - r 1) tanθ 1) is the center, and ( ) R - r 1) secθ 1+ r With a radius of 1, θ 2 is the central angle, with ( R - r 1+ r 1 cosθ 1, - r 1 sinθ 1) Draw the bottom spherical generatrix arc as the starting point. Arc e ; The circular arc of the toroidal surface generatrix Arc r and the bottom spherical generatrix arc Arc e The calculation formulas are respectively , , in x r , z r The circular arc of the generatrix of the toroidal surface. Arc r The coordinates of any point on the top, x e , z e The bottom spherical generatrix arc Arc r Coordinates of any point on the [top]; Step 3: Construct calculation formulas for tool parameters based on geometric relationships; remember( R - r 1+ r 1 cosθ 1, - r 1 sinθ 1) Let A be a point, and denote... r 2 = ( R - r 1) secθ 1+ r 1. Then the axial length of the tool tip D = r 2- O e O m , ; Step 4: Represent the generatrix arc of the annular surface and the generatrix arc of the bottom spherical surface as follows: R , D , θ The expression for 1; The radius of the generatrix arc of the annular torus is obtained from the calculation formula in step three. r 1 and the radius of the bottom spherical generatrix and arc generatrix r 2, , and the annular surface S r and the bottom spherical S e ; The annular surface of the ring S r and the bottom spherical surface S e The calculation formula is , , in θ For surface parameters, it is the angle between the radial line at any point on the tool surface and the Z-axis; φ For surface parameters, the radial line at any point on the tool surface and the radial line are... XOZ The angle between the surfaces X r , Y r , Z r For the annular surface S r The coordinates of any point on the top, X e , Y e , Z e The bottom sphere S e The coordinates of any point on the [above].

2. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end rotation surface according to claim 1, characterized in that: In step two θ 1 +θ 2= π / 2.

3. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end rotation surface according to claim 1, characterized in that: The positional relationship between the generatrix arc of the annular surface and the generatrix arc of the bottom spherical surface is that they are tangent.

4. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end rotation surface according to claim 1, characterized in that: The radius of the generatrix arc of the annular surface in step four. r 1 and the radius of the bottom spherical generatrix arc r 2 wraps Z The ring is formed by rotating the axis once. S r and the bottom spherical S e .

5. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end revolution surface according to claim 1, characterized in that: The end axial length in step three D Smaller than the radius of the tool holder R .

6. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end revolution surface according to claim 1, characterized in that: In step one, the radius of the bottom spherical generatrix arc is... r 2 is greater than the radius of the tool holder R .

7. The parametric design method for a milling cutter with a tangent circular arc as the generatrix of its end rotation surface according to claim 1, characterized in that: In step two, the central angle of the generatrix arc of the annular surface... θ The range of values ​​for 1 is 0 ≤ θ 1≤90 ° .

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