Waveform blade milling cutter for chatter suppression and method of designing the same

Abstract

The embodiment of the application provides a waveform blade milling cutter for chatter suppression and a design method thereof, the method comprising: a waveform blade curve of the milling cutter is a sinusoidal waveform blade curve or a cycloid waveform blade curve, the sinusoidal waveform blade curve is connected by sinusoidal segments, and the cycloid waveform blade curve is connected by cycloid segments; and the waveform blade curve rotates around a milling cutter shaft to form a waveform blade spiral curve. By adopting the sinusoidal waveform blade or the cycloid waveform blade, the whole cutting edge is a continuous cutting edge, all participates in cutting, the advantages of the waveform blade in reducing cutting force and breaking chips are fully played, and the waveform blade milling cutter designed based on the method can be applied to semi-finishing, finishing and other processes directly related to the quality of a final machining surface.

Description

Technical Field

[0001] This invention relates to the field of milling cutter design technology, specifically to a wave-edge milling cutter for chatter suppression and its design method. Background Technology

[0002] Milling cutters are essential tools for material removal in machining. Through the motion control of milling machines or machining centers, the cutter rotates, moves, and oscillates at high speeds to remove excess material from parts, ultimately yielding parts that meet design dimensions and precision requirements. Chatter during five-axis side milling of complex curved surfaces has a significant impact on the surface quality of the machined parts. Exacerbated chatter can damage the workpiece, cutting tool, and even the machine tool. By employing appropriate methods to improve the dynamics of side milling, enhance milling stability, and avoid chatter, machining quality and efficiency can be effectively improved.

[0003] Current technologies often employ unconventional milling cutters, such as variable pitch and variable helix angle milling cutters, to suppress chatter during milling. For example, Chinese patent application CN200520052955 proposes a wave-edge end mill that produces a sawing effect on the machined surface during rotary milling, achieving good chip breaking and removal, significantly increasing the feed rate and speed of the end mill, reducing tool breakage, and improving tool life; Chinese patent application CN201310232178 proposes a wave-edge end mill that processes the helical rake face into a wave-shaped helical surface, with the peaks and valleys of adjacent helical surfaces staggered along the axis by a certain distance, significantly reducing the cutting width, producing narrow and thick chips, reducing the degree of cutting deformation, mitigating the periodicity of cutting force changes, and making the cutting process smooth; Chinese patent application CN201920268459 proposes a serrated edge forming end mill for machining specific textures, which can achieve one-time forming of wave patterns formed by multiple identical arcs, ensuring the consistency of the wave pattern while improving machining efficiency. However, a common feature of the above-mentioned milling cutters is that the wave-shaped cutting edge is discontinuous. This results in discontinuous rake and flank faces of the formed cutting edge, making them only suitable for roughing operations that require a large amount of material removal. They are not suitable for semi-finishing and finishing operations, which are directly related to the final surface quality. Summary of the Invention

[0004] This invention provides a wave-shaped end mill for chatter suppression and its design method, in order to solve the problem that the prior art is not applicable to semi-finishing and finishing processes that are directly related to the final surface quality.

[0005] In a first aspect, embodiments of the present invention provide a design method for a wave-edge end mill for chatter suppression, comprising:

[0006] The wave-shaped cutting edge curve of the milling cutter can be a sine wave-shaped cutting edge curve or a cycloidal wave-shaped cutting edge curve. The sine wave-shaped cutting edge curve is formed by connecting sine segments, and the cycloidal wave-shaped cutting edge curve is formed by connecting cycloidal segments.

[0007] The wave-shaped cutting edge curve rotates around the milling cutter axis to form a wave-shaped spiral curve.

[0008] In one embodiment, when the waveform cutting edge curve of the milling cutter is a sinusoidal waveform cutting edge curve, a sinusoidal waveform cutting edge spiral curve is formed, and the sinusoidal waveform cutting edge curve satisfies the following expression:

[0009]

[0010] Among them, z 1s The x-axis value of the sinusoidal wave-shaped spiral curve is u. 1s The vertical coordinate value of the sinusoidal wave-shaped spiral curve is γ. js Let A be the helix angle of the j-th sinusoidal wave-shaped helical curve. j Let λ be the amplitude of the j-th cutting edge curve. j Let θ be the wavelength of the j-th cutting edge curve. j Let be the initial phase of the j-th cutting edge curve.

[0011] In one embodiment, when the wavy cutting edge curve of the milling cutter is a cycloidal wavy cutting edge curve, a cycloidal wavy cutting edge spiral curve is formed, and the cycloidal wavy cutting edge curve satisfies the following expression:

[0012]

[0013] Where r is the radius of the cycloidal base circle, t is the rolling angle of the cycloidal base circle, and γ jc Let z be the helix angle of the j-th cycloidal wave-edge helical curve. 1c u is the abscissa value of the cycloidal wave-edge helical curve. 1c Z represents the ordinate value of the cycloidal wave-shaped helical curve. j Let be the initial moving distance of the j-th cutting edge curve.

[0014] In one embodiment, the method further includes adding a straight line segment at the starting end of the waveform curve.

[0015] In one embodiment, the line segment satisfies the following expression:

[0016]

[0017] Among them, z l u is the x-coordinate of the line segment. lz1 is the ordinate of the line segment, z2 is the abscissa of the intersection of the line segment and the wave-shaped curve, u1 is the ordinate of the intersection of the line segment and the wave-shaped curve, z0 is the abscissa of the intersection of the line segment and the coordinate axis, and u0 is the ordinate of the intersection of the line segment and the coordinate axis.

[0018] In one embodiment, straight segments are alternately arranged on the wave-shaped cutting edge curve of the milling cutter.

[0019] In one embodiment, straight segments are continuously arranged on the wave-shaped cutting edge curve of the milling cutter, and the lengths of the straight segments arranged on adjacent cutting edges are different.

[0020] In one embodiment, the projected length of the straight line segment on the virtual spiral is less than the waveform length of the sine segment or the cycloidal segment.

[0021] In one embodiment, the number of wave blade curves is two, three, or four.

[0022] Secondly, embodiments of the present invention provide a wave-edge end mill for chatter suppression, designed using the wave-edge end mill design method for chatter suppression as described in any of the first aspects.

[0023] The wave-edge end mill and its design method for chatter suppression provided in this invention embodiment feature a wave-edge curve that is either a sinusoidal or cycloidal. The sinusoidal wave-edge curve is formed by connecting sinusoidal segments, while the cycloidal wave-edge curve is formed by connecting cycloidal segments. The wave-edge curve rotates around the end mill's axis to form a wave-edge helical curve. By employing a sinusoidal or cycloidal wave-edge, the entire cutting edge is a continuous cutting edge, participating in cutting. This fully leverages the advantages of wave-edges in reducing cutting forces and chip breaking, allowing the wave-edge end mill designed based on this method to be applied to semi-finishing and finishing processes directly related to the final machined surface quality. Attached Figure Description

[0024] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0025] Figure 1 A flowchart illustrating a design method for a wave-edge end mill for chatter suppression according to an embodiment of the present invention;

[0026] Figure 2 A schematic diagram of the geometric modeling of the waveform blade curve provided in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of a sinusoidal wave blade curve provided in an embodiment of the present invention;

[0028] Figure 4This is a schematic diagram of the cycloidal waveform blade curve provided in an embodiment of the present invention;

[0029] Figure 5 This is a schematic diagram showing the unfolded sinusoidal wave blade curve and cycloidal wave blade curve according to an embodiment of the present invention;

[0030] Figure 6 A three-dimensional diagram of a wave-shaped end mill provided in an embodiment of the present invention;

[0031] Figure 7 A comparison of the milling stability of a wave-shaped end mill provided in an embodiment of the present invention at a radial penetration ratio of 20%;

[0032] Figure 8 A comparison of the stability of milling operations with a wave-shaped end mill provided in an embodiment of the present invention at a radial penetration ratio of 5%;

[0033] Figure 9 Comparison of flap diagrams showing the milling stability of a wave-shaped end mill provided in an embodiment of the present invention at a radial penetration ratio of 50%.

[0034] Explanation of reference numerals in the attached figures:

[0035] 1-Handle, 2-Cutting edge, 201-Sine wave edge, 201a-Sine segment, 201b-Sine straight segment, 2011-First sine wave edge, 2012-Second sine wave edge, 2013-Third sine wave edge, 2014-Fourth sine wave edge, 2015-Virtual spiral I, 202-Cycloidal wave edge, 202a-Cycloidal segment, 202b-Cycloidal straight segment, 202c-Cycloidal base circle, 2021-First cycloidal wave edge, 2022-Second cycloidal wave edge, 2023-Third cycloidal wave edge, 2024-Fourth cycloidal wave edge, 2025-Virtual spiral II.

[0036] The accompanying drawings have illustrated specific embodiments of the invention, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of this application. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to this application are not shown or described in the specification. This is to avoid obscuring the core parts of this application with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0038] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.

[0039] The serial numbers assigned to components in this document, such as "first" and "second," are used only to distinguish the described objects and have no sequential or technical meaning. The terms "connection" and "linkage" used in this application, unless otherwise specified, include both direct and indirect connections (linkages).

[0040] The wavy-edged milling cutters involved in the prior art are usually designed for chip breaking, chip removal, reducing cutting load, and machining specific textures. Their wavy edges are discontinuous, which leads to discontinuities in the rake face and flank face that form the cutting edge. They are only suitable for roughing operations that require a large amount of material removal, and are not suitable for semi-finishing or finishing operations that are directly related to the final surface quality.

[0041] Wave-edge end mills possess both locally variable pitch and variable helix angle characteristics along their axis, making them highly promising for chatter suppression in milling operations. However, existing technologies have not addressed the role of wave-edge end mills in chatter suppression, lacking corresponding design methods and related products. This application fully explores the potential of wave-edge end mills in chatter suppression, proposing a wave-edge end mill for chatter suppression and its design method. Specific embodiments will be used to illustrate this application in detail below.

[0042] Figure 1 This is a flowchart illustrating a design method for a wave-edge end mill used for chatter suppression, provided as an embodiment of the present invention. Figure 1As shown, the design method for a wave-edge end mill for chatter suppression provided in this embodiment may include:

[0043] S101. The wave-shaped cutting edge curve of the milling cutter is either a sine wave cutting edge curve or a cycloidal wave cutting edge curve. The sine wave cutting edge curve is formed by connecting sine segments, and the cycloidal wave cutting edge curve is formed by connecting cycloidal segments.

[0044] S102, the wave-shaped cutting edge curve rotates around the milling cutter axis to form a wave-shaped cutting edge spiral curve.

[0045] Please refer to Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, the wave-edge curves of the wave-edge end mills used for chatter suppression are either sinusoidal wave-edges (201) or cycloidal wave-edges (202), respectively formed by connecting sinusoidal segments (201a) or cycloidal segments (202a). The wave-edge curves rotate around the end mill axis at a fixed helix angle to form a wave-edge helical curve: sinusoidal wave-edge curve (as shown in the image). Figure 3 (as shown) or cycloidal wave blade curve (such as) Figure 4 As shown). Its unfolding is as follows. Figure 5 As shown.

[0046] The wave-edge end mill design method for chatter suppression provided in this embodiment uses a sinusoidal or cycloidal wave-edge to make the entire cutting edge a continuous cutting edge that participates in cutting. This fully leverages the advantages of wave-edges in reducing cutting force and chip breaking, allowing wave-edge end mills designed based on this method to be applied to semi-finishing and finishing processes that are directly related to the final surface quality.

[0047] Based on the above embodiments, the following will provide specific descriptions of sinusoidal and cycloidal wave cutting edges. By using a sine curve or a piecewise cycloid with a simple functional expression to construct the wave curve of the milling cutter, the cutting edge curve can be easily expressed, facilitating the design and manufacturing of the cutting edge.

[0048] In one optional implementation, when the waveform cutting edge curve of the milling cutter is a sinusoidal waveform cutting edge curve, a sinusoidal waveform cutting edge spiral curve is formed, and the sinusoidal waveform cutting edge curve satisfies the following expression:

[0049]

[0050] Among them, z 1s The x-axis value of the sinusoidal wave-shaped spiral curve is u. 1s The vertical coordinate value of the sinusoidal wave-shaped spiral curve is γ. js Let A be the helix angle of the j-th sinusoidal wave-shaped helical curve. j Let λ be the amplitude of the j-th cutting edge curve. jLet θ be the wavelength of the j-th cutting edge curve. j Let j be the initial phase of the j-th cutting edge curve. It should be noted that j is a natural number less than or equal to N, and N is the number of wave-shaped cutting edge curves.

[0051] Specifically, for the sinusoidal segment (201a) of the sinusoidal wave blade (201), assuming that the amplitude, wavelength, and initial phase of the j-th blade curve are A j , λ j and θ j Then the expression for the sine segment (201a) is:

[0052]

[0053] In equation (1), z 0s and u 0s These are the horizontal and vertical coordinates of the sine segment (201a). The expression for the sinusoidal spiral curve formed by rotating this curve around the milling cutter axis is:

[0054]

[0055] In equation (ii), z 1s and u 1s The x and y coordinates of the sinusoidal wave blade (201) spiral curve are respectively, γ js Let be the helix angle of the j-th sinusoidal wave-edge helical curve, which is represented by the corresponding virtual helix I (2015). Rearranging equation (II) yields:

[0056]

[0057] Finally, substituting equation (III) into equation (I) yields the expression for the sinusoidal waveform cutting edge curve:

[0058]

[0059] In one optional implementation, when the wavy cutting edge curve of the milling cutter is a cycloidal wavy cutting edge curve, a cycloidal wavy cutting edge spiral curve is formed, and the cycloidal wavy cutting edge curve satisfies the following expression:

[0060]

[0061] Where r is the radius of the cycloidal base circle, t is the rolling angle of the cycloidal base circle, and γ jc Let z be the helix angle of the j-th cycloidal wave-edge helical curve. 1c u is the abscissa value of the cycloidal wave-edge helical curve. 1c Z represents the ordinate value of the cycloidal wave-shaped helical curve. j Let be the initial moving distance of the j-th cutting edge curve.

[0062] Specifically, for the cycloidal segment (202a) of the cycloidal wave blade (202), assuming the radius of the cycloidal base circle (202c) is r, the expression for the cycloidal segment (202a) is:

[0063]

[0064] In equation (5), t is the rolling angle of the cycloidal base circle (202c), and z j Let z be the initial moving distance of the j-th cutting edge curve. 0c and u 0c These are the horizontal and vertical coordinates of the cycloidal segment (202a). The expression for the cycloidal wave-shaped spiral curve formed by rotating this curve around the milling cutter axis is:

[0065]

[0066] In equation (vi), γ jc Let be the helix angle of the j-th cycloidal wave edge (202) helical curve, which is represented by the corresponding virtual helix II (2025). Substituting equation (v) into equation (vi) yields the expression for the cycloidal wave edge curve:

[0067]

[0068] In equations (iv) and (vii) above, besides the independent variable t, equation (vii) has only one independent parameter r, and the wavelength 4πr is only related to r. However, the sine curve, in addition to the independent variable t, has two other independent parameters A. j and wavelength λ j Each can be adjusted separately.

[0069] Based on any of the above embodiments, in order to further adjust the local helix angle between adjacent cutting edges (the tangential direction v at the current point)... j，i (Angle between the direction of the cutter axis and the tooth pitch P) i To enhance the continuous regeneration delay effect between adjacent cutting edges, in an optional embodiment, a straight line segment can be added at the starting end of the wavy cutting edge curve. For a sinusoidal wavy cutting edge curve, a sinusoidal straight line segment is added; for a cycloidal wavy cutting edge curve, a cycloidal straight line segment is added. Specifically, the expression for the straight line segment is:

[0070]

[0071] Among them, z l u is the x-coordinate of the line segment. lLet z0 be the ordinate of the line segment, z1 be the abscissa of the intersection of the line segment and the wave-shaped curve, u1 be the ordinate of the intersection of the line segment and the wave-shaped curve, z0 be the abscissa of the intersection of the line segment and the coordinate axis, and u0 be the ordinate of the intersection of the line segment and the coordinate axis. In Equation (VIII), z0... i and u j z1 and u1 are the coordinates of the intersection point of the straight line segment and the wave blade curve, respectively, i.e., the coordinates of the starting point of the wave blade segment, obtained by equation (iv) or equation (vii). z0 and u0 are the coordinates of the intersection point of the straight line segment and the coordinate axis, respectively, which can be obtained by equation (i) or equation (v). j and initial movement distance z j To determine.

[0072] Optionally, straight segments can be alternately set on the wave-shaped cutting edge curves of the milling cutter. Taking a number of four sine wave-shaped cutting edge curves as an example (the first, second, third, and fourth sine wave-shaped cutting edges respectively), straight segments can be set on the first and third sine wave-shaped cutting edges, or on the second and fourth sine wave-shaped cutting edges.

[0073] Optionally, straight segments can be continuously set on the wave-shaped cutting edge curve of the milling cutter, and the lengths of the straight segments on adjacent cutting edges can be different (to increase the multi-delay effect between adjacent cutting teeth). Taking a four-sinusoidal wave-shaped cutting edge curve as an example (first, second, third, and fourth sinusoidal wave-shaped cutting edges respectively), a first straight segment can be set on the first sinusoidal wave-shaped cutting edge, a second straight segment on the second sinusoidal wave-shaped cutting edge, a third straight segment on the third sinusoidal wave-shaped cutting edge, and a fourth straight segment on the fourth sinusoidal wave-shaped cutting edge. The lengths of the first and second straight segments are different, the lengths of the second and third straight segments are different, the lengths of the third and fourth straight segments are different, and the length of the fourth straight segment is different from the first straight segment.

[0074] Furthermore, the projected length of the straight line segment on the virtual spiral is less than the waveform length of the sine segment or cycloid segment.

[0075] Considering the chip removal effect and actual application scenarios, the number of wave-shaped blade curves can be two, three, or four. Taking four as an example, they are represented as: the first sine wave blade (2011), the second sine wave blade (2012), the third sine wave blade (2013), and the fourth sine wave blade (2014), or the first cycloidal wave blade (2021), the second cycloidal wave blade (2022), the third cycloidal wave blade (2023), and the fourth cycloidal wave blade (2024).

[0076] The method provided in this embodiment adds a straight blade at the beginning of the wave-shaped blade curve to adjust the phase difference between adjacent blades in the axial direction, thereby controlling the local tooth angle and helix angle and enhancing the continuous regeneration delay effect of the blade.

[0077] At any axial height u of the wave-shaped end mill i At point P, the local tooth spacing between two adjacent wave-shaped cutting edges j and j+1 i It can be represented as:

[0078] P i =|z j+1，i -z j，i (ix)

[0079] Among them, z j+1，i and z j，i Let x and y be the x-coordinates of the (j+1)th and jth wave edges, respectively. Then, let P... i The corresponding local tooth angle θ j，i and the local helix angle of the j-th wave edge (i.e., the tangent vector v of the corresponding j-th wave edge) j，i The angles between the milling cutter axis and the milling cutter axis are expressed as follows:

[0080]

[0081] Where R is the radius of the wave-shaped end mill, du j,i / dz j,i For u i The first derivative of the waveform curve at the height can be obtained from equations (iv), (vii), and (viii) based on the actual waveform function. Therefore, equations (iv), (vii), (viii), (ix), and (x) establish the local tooth angle and local helix angle of adjacent waveform edges at any axial height for the waveform end mill. By introducing a non-constant helix angle and tooth spacing that vary periodically along its axial direction through the waveform edge, the introduction of locally variable helix angle and locally variable tooth spacing is realized, increasing the multi-delay effect between adjacent teeth, disrupting the phase difference between the current tooth and the previous tooth during the cutting process, that is, disrupting the regeneration effect and improving the stability of the cutting process.

[0082] By associating with the milling dynamics model, the optimized parameters of the wave-edge end mill can be obtained through inverse solving based on the milling stability requirements. These parameters include the virtual helix angle, the number of wave edges, and the parameters of each wave edge. During the milling dynamics solution, the end mill can be divided into several micro-element thicknesses (u) along the axial direction. j+1,i -u j,i At this time, u can be used. j+1,i and u j,i Average at two axial heights and Substitute the values ​​into the above equations to solve.

[0083] In summary, the wave-edge end mill design method for chatter suppression provided in this application, through the use of sinusoidal or cycloidal wave edges, ensures that the entire cutting edge is a continuous cutting edge, participating in the cutting process. This fully leverages the advantages of wave edges in reducing cutting forces and chip breaking, and can be applied to processes directly related to the final surface quality, such as semi-finishing or finishing. The wave edge introduces a non-constant helix angle and tooth spacing that vary periodically along its axial direction, simultaneously achieving localized variable helix angles and tooth spacings. This increases the multi-delay effect between adjacent teeth, disrupting the cutting process. The phase difference between the current cutting tooth and the previous cutting tooth disrupts the regeneration effect and improves the stability of the cutting process. This differs from common variable helix end mills with a fixed helix angle on each tooth. The wavy cutting edge curve of the end mill is constructed using a sine curve or piecewise cycloid with a simple functional expression, making the cutting edge curve easy to express and facilitating its design and manufacturing. By adding a straight cutting edge at the beginning of the wavy cutting edge curve, the phase difference between adjacent cutting edges in the axial direction can be adjusted, achieving local control of the inter-tooth angle and helix angle to enhance the continuous regeneration delay effect of the cutting edge. This is beneficial for suppressing milling chatter and has great application potential in high-quality, high-efficiency machining of parts.

[0084] This invention also provides a wave-edge end mill for chatter suppression, designed using the wave-edge end mill design method for chatter suppression described in any of the preceding embodiments. Please refer to its three-dimensional diagram. Figure 6 As shown, the wave-shaped end mill provided in this embodiment has four cutting edges.

[0085] The performance of the wave-edge end mill for chatter suppression and its design method provided in this application will be further illustrated below with specific examples.

[0086] Example 1: Using two types of wave-shaped end mills, namely sine wave cutter 201 and cycloidal wave cutter 202, the amplitude of the sine segment 201a is made the same as the amplitude of the cycloidal segment 202a. The wave-shaped end mills are shown in the attached figure. Figure 6 As shown in Table 1, a conventional variable pitch variable helix angle end mill was also used for comparison. The geometric parameters of the end mill's cutting edge are shown in Table 1. The conventional variable pitch variable helix angle end mill used is a commonly used four-flute helical end mill, with the tooth spacing of its four teeth being [70° 110° 70° 110°] and the helix angles being [30° 35° 30° 35°]. For end mills with different cutting edge curves, the corresponding milling stability lobe diagrams were obtained, and the effect of the wave-shaped cutting edge end mill proposed in this application on chatter suppression was compared accordingly. The milling dynamic parameters of the two-degree-of-freedom system used for stability lobe diagram prediction are shown in Table 2.

[0087] Table 1. Geometric parameters of the milling cutter cutting edge

[0088]

[0089] Table 2 Milling Dynamics Parameters of Two-DOF System

[0090] Parameter name numerical values Modal mass (kg) <![CDATA[m x =1.4986,m y =1.1990]]> Relative damping ratio (%) <![CDATA[ζ x =5.58,g y =2.50]]> Natural frequency (Hz) <![CDATA[w 0x =563.60,w 0y =516.21]]> <![CDATA[Cutting force coefficient (N / m 2 )]]> <![CDATA[K t =6.97×10 8 ,K n =2.56×10 8 ]]>

[0091] m in Table 2 x The modal mass in the x-direction is represented by m. y Represents the modal mass in the y-direction; ζ x ζ represents the relative damping ratio in the x-direction. y Indicates the relative damping ratio in the y-direction; w 0x representing the natural frequency in the x-direction, w 0y K represents the natural frequency in the y-direction. t K represents the cutting force coefficient in the tangential direction. n The cutting force coefficient in the normal direction.

[0092] The stability lobe diagram was solved for a spindle speed range of 2000–15000 rpm and an axial depth of cut range of 0–40 mm, discretized into a 50×50 solution mesh. Two stability lobe diagrams were obtained with radial penetration ratios (the ratio of radial depth of cut to tool diameter) of 20% and 5%, respectively, as shown in the attached diagram. Figure 7 and attached Figure 8 As shown. The area below each leaf-shaped curve represents the corresponding range of axial depth of cut and spindle speed for stable, chatter-free cutting, while the area above the curve represents the range of unstable cutting parameters that would cause chatter. Figure 7 and Figure 8 It can be seen that, compared with conventional variable pitch and variable helical cutting edge end mills, the two end mills proposed in this application, the sinusoidal wave cutting edge 201 and the cycloidal wave cutting edge 202, both achieve significantly improved stable cutting domains, especially in terms of the limiting axial depth of cut and the spindle speed range. When the radial penetration ratio is 20% (see attached diagram) Figure 7 The limiting axial depth of cut for a variable pitch, variable helical cutting edge end mill is approximately 17.5 mm, corresponding to a spindle speed of approximately 5000 rpm, while the limiting axial depth of cut for a wave-shaped cutting edge end mill is approximately 27.5 mm, corresponding to a spindle speed of approximately 7000 rpm. The limiting axial depth of cut and spindle speed are increased by approximately 57% and 40%, respectively. When the radial penetration ratio is 5% (see attached...). Figure 8The increase in the ultimate axial depth of cut is greater, corresponding to a spindle speed increase of approximately 40%. Furthermore, comparing the stability flap diagrams for two different radial penetration ratios reveals that, at a smaller radial penetration ratio, the wave-shaped cutting end mill proposed in this application exhibits a wider and higher spindle speed range (6000–8000 rpm) near the ultimate axial depth of cut, while the variable pitch, variable helix cutting end mill corresponds to a spindle speed range of only approximately (4000–5000 rpm). In other words, to achieve a greater ultimate axial depth of cut, the spindle speed increases by approximately 50%, and the speed range doubles.

[0093] Example 2: The sinusoidal wave-shaped cutting edge 201 and the cycloidal wave-shaped cutting edge 202 are compared with conventional equal-pitch, equal-helix-angle cutting edge end mills. The cutting edge curve parameters are the same as in Example 1, as shown in Table 1. The selected equal-pitch, equal-helix-angle cutting edge end mills all have a tooth pitch of 90° and a helix angle of 30°. The milling stability lobe diagrams for each type of end mill are obtained to compare the effectiveness of the wave-shaped cutting edge end mills proposed in this application in chatter suppression. The milling dynamics parameters of the two-degree-of-freedom system used for lobe diagram prediction are shown in Table 3.

[0094] Table 3 Milling Dynamics Parameters of Two-DOF System

[0095] Parameter name numerical values Modal mass (kg) <![CDATA[m x =1.4986,m y =1.1990]]> Relative damping ratio (%) <![CDATA[ζ x =3.08,g y =4.37]]> Natural frequency (Hz) <![CDATA[w 0x =711,w 0y =509]]> <![CDATA[Cutting force coefficient (N / m 2 )]]> <![CDATA[K t =2.34×10 8 ,K n =3.52×10 8 ]]>

[0096] The stability lobe diagram was solved with a spindle speed range of 2000–7000 rpm and an axial depth of cut of 0–25 mm, discretized into a 50×50 solution mesh, yielding a stability lobe diagram with a radial intrusion ratio of 50%, as shown in the attached diagram. Figure 9 As shown. By Figure 9 It can be seen that, compared with end mills with equal tooth pitch and equal helical cutting edges, the two end mills proposed in this application, the sinusoidal waveform cutting edge 201 and the cycloidal waveform cutting edge 202, significantly improve the stable cutting range across the entire cutting surface, and the lower boundary of the stable range is also significantly increased. Specifically, the sinusoidal waveform cutting edge 201 primarily improves the limiting axial depth of cut, while the cycloidal waveform cutting edge 202 primarily improves the lower boundary of the stable range. Specifically, the limiting axial depth of cut at a spindle speed of 3500 rpm is increased by approximately 80%. Simultaneously, the lower boundary of the stable range is improved by approximately 75% across the entire cutting range.

[0097] The above results demonstrate that by using the wave-shaped cutting edge end mill proposed in this application, chatter-free stable cutting can be achieved with a larger axial depth of cut, higher spindle speed, and a wider spindle speed range. Therefore, the wave-shaped cutting edge end mill proposed in this application can be used in semi-finishing and finishing processes, significantly improving the machining efficiency and quality of part surfaces. These advantages are attributed to the wave-shaped cutting edge design, which simultaneously introduces local variable pitch and variable helix angle at different axial heights, increasing the multi-delay effect between adjacent teeth and disrupting the phase difference between the current tooth and the previous tooth during cutting, thus disrupting the regeneration effect and improving cutting stability.

[0098] This invention also provides a computer-readable storage medium storing a computer program thereon, which is executed by a processor to implement the technical solutions of any of the above method embodiments.

[0099] The various embodiments in this disclosure are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0100] The scope of protection of this disclosure is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from its scope and spirit. If such modifications and variations fall within the scope of the claims of this disclosure and their equivalents, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A method of designing a wave form blade mill for chatter suppression, characterized by, The application relates to a design method of a wave-shaped blade milling cutter for chatter suppression. The wave-shaped blade curve of the milling cutter is a sinusoidal wave-shaped blade curve or a cycloidal wave-shaped blade curve, the sinusoidal wave-shaped blade curve is connected by sinusoidal segments, and the cycloidal wave-shaped blade curve is connected by cycloidal segments; The wave-shaped blade curve rotates around a milling cutter shaft to form a wave-shaped blade helix curve; A straight segment is added at the starting end of the wave-shaped blade curve, the straight segments are alternately arranged on the wave-shaped blade curve of the milling cutter, or the straight segments are continuously arranged on the wave-shaped blade curve of the milling cutter and the lengths of the straight segments arranged on adjacent blade edges are different; The projection length of the straight segment on a virtual helix line is smaller than the wave length of the sinusoidal segment or the cycloidal segment.

2. The method of claim 1, wherein, When the wave-shaped blade curve of the milling cutter is a sinusoidal wave-shaped blade curve, a sinusoidal wave-shaped blade helix curve is formed, and the sinusoidal wave-shaped blade edge curve satisfies the following expression: in, The x-axis value is the sinusoidal wave-shaped spiral curve. The vertical coordinate value is the ordinate value of the sinusoidal wave-shaped spiral curve. For the first The helix angle of a sinusoidal wave-shaped helical curve. For the first The amplitude of the cutting edge curve, For the first The wavelength of the cutting edge curve, For the first The initial phase of the cutting edge curve.

3. The method of claim 1, wherein, When the wave-shaped blade curve of the milling cutter is a cycloidal wave-shaped blade curve, a cycloidal wave-shaped blade helix curve is formed, and the cycloidal wave-shaped blade edge curve satisfies the following expression: wherein, is a radius of a base circle of the cycloid, is a rolling angle of the base circle of the cycloid, is a first is a spiral angle of the cycloid wave blade spiral curve, is an abscissa value of the cycloid wave blade spiral curve, is an ordinate value of the cycloid wave blade spiral curve, is a first is an initial moving distance of the blade edge curve.

4. The method of claim 1, wherein, The straight segment satisfies the following expression: wherein is a horizontal coordinate value of the intersection point of the straight line segment and the wave-shaped blade curve, is a vertical coordinate value of the intersection point of the straight line segment and the wave-shaped blade curve, is a horizontal coordinate value of the intersection point of the straight line segment and the wave-shaped blade curve, is a vertical coordinate value of the intersection point of the straight line segment and the wave-shaped blade curve, is a horizontal coordinate value of the intersection point of the straight line segment and the coordinate axis, is a vertical coordinate value of the intersection point of the straight line segment and the coordinate axis.

5. The method according to any one of claims 1 to 4, characterized in that, The number of the wave-shaped blade curves is two, three or four.

6. A wave form blade milling cutter for chatter suppression, characterized by, The wave-shaped blade milling cutter for chatter suppression is designed by the design method.

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