Flutter suppression milling cutter design method and cutter
By adopting a hyperbolic arc structure and passivation treatment in the milling tool design, the chatter problem in the milling process of thin-walled parts was solved, and the machining stability and surface quality were improved.
Patent Information
- Application Number
- CN202610061541.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-16
- Publication Date
- 2026-05-01
Smart Images
Figure CN121959932A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of cutting design technology, specifically to a chatter suppression milling tool design method and tool. Background Technology
[0002] Chatter, also known as cutting vibration or chattering, is a typical machining instability phenomenon caused by the cutting force during the milling of thin-walled or weakly rigid parts. Its main characteristic is periodic vibration between the tool and the workpiece, leading to reduced surface quality, accelerated tool wear, and potentially damage to the machine tool. The presence of chatter not only weakens the assembly accuracy and performance of the product but also significantly increases the cost and difficulty of post-processing steps.
[0003] Chatter is an undesirable phenomenon that occurs during machining and should be minimized or avoided. Common methods to reduce chatter include shortening the tool overhang, selecting a more rigid tool holder, reducing the depth of cut or radial width, reducing cutting force, and strengthening workpiece clamping, such as adding supports, using damping tools, such as vibration-damping boring bars or variable helix end mills, layered cutting, or climb milling. However, these methods inevitably increase workload, extend machining time, and may even lead to workpiece scrap.
[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0005] The purpose of this invention is to provide a chatter suppression milling tool design method and tool to solve the problems mentioned in the background art.
[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for designing milling tools to suppress chatter, comprising the following steps: Based on the diameter and shank length of the milling cutter to be produced, a cylindrical tool model is constructed. The tool model includes a shank part and a cutting edge part. In the cutting edge part, a scanning cut is performed along the generatrix of the tool model to obtain several peripheral cutting edges parallel to the generatrix of the tool model. The chip groove structure is drawn based on the position of the outer peripheral edge to form the corresponding bottom edge of the tool. The corresponding outer peripheral edge and the bottom edge of the tool are connected by the hyperbolic arc segment of the tool tip. The tangent points of the hyperbolic arc segment of the tool tip with the bottom edge and the outer peripheral edge are determined respectively. The radial distance of the two tangent points along the radial direction of the tool model and the axial distance along the axial direction of the tool model are analyzed. The expression of the hyperbolic arc segment of the tool tip is constructed and transformed into the standard equation of the hyperbola through coordinate transformation. Based on the standard equation of a hyperbola, and with the radial and axial distances being equal as constraints, the shape parameters of the hyperbola segment at the cutting edge are constrained to determine the range of shape parameters for the hyperbola segment at the cutting edge, thereby determining the specific shape of the hyperbola segment at the cutting edge. Using a hyperbolic linear structure, the bottom edge, outer peripheral edge, and connected tip hyperbolic arc segment of the tool are blunted. Specifically, the second shape parameters of the cutting edge hyperbolic arc segment are determined by combining the tangent parallel to the tool axis at the tip point and the edge line at the tip point in the first flank face of the bottom edge. The blunting process is completed through the cutting edge hyperbolic arc segment. The blunted outer peripheral edge is then twisted to obtain a helical structure of several outer peripheral edges, thereby completing the structural design of the milling tool.
[0007] Furthermore, the specific method for scanning and cutting the cutting edge is as follows: determine the vertical center line of the milling cutter body, which is denoted as the generatrix of the tool model. Using the generatrix as the cutting path, scan and cut along the direction of the generatrix to form an even number of peripheral cutting edges parallel to the generatrix of the milling cutter body, which are the cutting edges of the milling cutter.
[0008] Furthermore, the logic underlying the construction of the hyperbolic arc expression for the tool tip is as follows: A first coordinate system is constructed with the tool tip vertex of the tool model as the origin. The bottom cutting edge and outer peripheral cutting edge corresponding to this vertex are determined. The coordinates of the tangent points between the hyperbolic arc segment of the tool tip and the bottom cutting edge and outer peripheral cutting edge are determined respectively. The tangent point between the hyperbolic arc segment of the tool tip and the bottom cutting edge is denoted as tangent point A, with coordinates [missing information]. The point of tangency between the hyperbolic arc segment of the blade tip and the outer peripheral cutting edge is denoted as tangency point B, with coordinates as follows: ,in The diameter of the milling cutter to be manufactured. The radial distance between the hyperbolic arc segment of the tool tip and the point of tangency of the bottom cutting edge along the radial direction of the tool model. The distance between the hyperbolic arc segment of the tool tip and the tangent point of the outer peripheral edge along the axis of the tool model; For coordinates tangent to the positive semi-axis of the horizontal axis and the positive semi-axis of the vertical axis and The conic section, with its implicit function expression, is: In the formula, y and y' are the x and y coordinates of the hyperbola segment at the tip of the knife in the first coordinate system, respectively. Let be the shape parameters of the hyperbolic arc segment of the blade tip, where Use this implicit function expression as the initial expression for the hyperbola segment at the tip of the knife.
[0009] Furthermore, the logic behind transforming it into the standard equation of a hyperbola through coordinate transformation is as follows: the origin of the first coordinate system is moved to... At this point, and by flipping the x-axis, we obtain the second coordinate system as follows: ,in Let x be the x-coordinate of the second coordinate system. Let be the ordinate of the second coordinate system, and the mapping relationship between the coordinates of the first coordinate system and the second coordinate system is as follows: , Then the coordinates of the tangent point A are The coordinates of the tangent point B are The hyperbolic arc segment of the blade tip is transitionally connected to tangent points A and B in the second coordinate system. Based on the initial expression of the hyperbolic arc segment of the blade tip, the expression of the hyperbolic arc segment of the blade tip in the second coordinate system is: Will , Substituting the values, we obtain the standard equation of the hyperbola for the arc segment of the hyperbola. The specific expression for the standard equation of the hyperbola for the arc segment of the hyperbola is as follows: in, The range of values for the abscissa in the standard equation of a hyperbola is defined as follows: The range of values for the ordinate is .
[0010] Furthermore, the constraint that the radial distance and axial distance are the same is specifically expressed as follows: Using a symmetrical hyperbola for arc transitions, ,remember Given the tangent length, the expression for the standard equation of the hyperbola of the knife-tip hyperbola segment is transformed into: Simplified to: In the formula, The specific value depends on the diameter of the blade. The range of values is determined by the tangent length. The range of values for is substituted into the simplified expression of the standard hyperbola equation for the hyperbola segment to determine the shape parameters of the hyperbola segment at the knife tip. The range of values for .
[0011] Furthermore, determining the specific steps of the hyperbolic arc segment of the cutting edge includes: the logic of the passivation process is as follows: the point of the cutting tip closest to the tool's bottom cutting edge and the tool's rotation center is recorded as the passivation start point, and the point of connection between the end of the outer peripheral cutting edge and the tool holder is recorded as the passivation end point; Determine the tangent line parallel to the tool axis through the tool tip point, based on the closest point between the tool's bottom cutting edge and the tool's rotation center. The edge line of the first back face of the bottom edge passing through the tip of the blade. Tangent Parallel to the tool axis and along the edge line In a plane, the hyperbolic arc segment of the cutting edge is composed of a line that... and The cross section formed by the tangent hyperbola is formed by scanning removal. The entire path formed by the bottom edge of the tool, the hyperbola arc segment at the tip of the tool, and the outer peripheral edge is the passivation scanning removal path. Intersect the extension line of the chip groove edge with the tangent. The intersection point is taken as the origin of the coordinate system, and the direction away from the bottom edge of the tool is taken as the positive semi-axis. The tangent line and edge line Establish a third coordinate system within the first quadrant of the Cartesian coordinate system, and mark the coordinates of the blunting starting point in the third coordinate system as follows: H is the ordinate of the passivation starting point in the third coordinate system, then the tangent line... The equation is expressed as: In the formula, Tangent The x-coordinate in the third coordinate system; edge line The equation is expressed as: In the formula, For the edge line In the ordinate of the third coordinate system, Tangent With the edge line The angle between them.
[0012] Furthermore, based on tangent and edge line The equation expression is given, and the equation expression is normalized. The normalized value represents the directed distance from the point to the line. The specific formula used for normalization is as follows: In the formula, Tangent The normalized value, For the edge line The normalized value; Because the hyperbolic arc segment of the cutting edge is located on the edge line Below, therefore in order to The value is positive in the region where the hyperbolic arc segment of the cutting edge is located, therefore To take a negative value, the expression is: .
[0013] Furthermore, based on tangent and edge line Based on the normalized values and their respective tangent lengths, the general implicit function equation for the hyperbola segment of the cutting edge is constructed as follows: In the formula, To blunt the hyperbolic arc segment from the starting coordinates to the cutting edge and the tangent Distance between tangent points To blunt the hyperbolic arc segment from the starting coordinates to the edge and the edge line The distance between the points of tangency will affect the tangent line. and edge line Substituting the normalized value into the general implicit function equation of the hyperbolic arc segment of the cutting edge, we obtain the specific equation expression of the hyperbolic arc segment of the cutting edge: In the formula, The shape parameters of the hyperbolic arc segment of the cutting edge.
[0014] The present invention also provides a chatter suppression milling tool, which is manufactured by performing the above-described chatter suppression milling tool design method.
[0015] Compared with the prior art, the beneficial effects of the present invention are: This solution adopts a hyperbolic arc transition end mill structure. The hyperbolic structure is used at the tip and the cutting edge, which effectively reduces chatter from the structural design. No additional processing or auxiliary facilities are required to improve the smoothness of the cutting process, thereby achieving the goal of improving the surface quality of the machined part. In addition, the present invention uses a hyperbolic structure to blunt the tip and cutting edge of conventional milling cutters. This structure can reduce cutting chatter and improve the cutting stability of the tool by reducing the influence of airflow generated during tool cutting and dispersing cutting force. Attached Figure Description
[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a diagram illustrating the milling cutter of the present invention; Figure 3 This is a development diagram of the milling cutter thread of the present invention; Figure 4 This invention is a microscopic image of a milling cutter head; Figure 5 This is a cross-sectional view of the milling cutter of the present invention.
[0017] In the diagram: D is the diameter of the end mill. Helix angle peripheral blade, Peripheral first posterior face, Second flank face on the outer periphery, U-shaped chip groove The first back face of the bottom edge, The second back face of the bottom edge, Hyperbolic arc segment of the blade tip Tool bottom edge, e-chip groove edge, A tangent line passing through the tool tip and parallel to the tool axis. The edge line passing through the tip point on the first flank face of the bottom edge; M: the tip point of the bottom edge near the center of tool rotation; N: the contact transition point between the outer peripheral edge and the tool holder; B: the tangent point between the hyperbolic arc segment of the tip and the outer peripheral edge; A: the tangent point between the hyperbolic arc segment of the tip and the bottom edge of the tool. The radial distance between the hyperbolic arc segment of the tool tip and the tangent point of the bottom cutting edge along the radial direction of the tool model. The axial distance between the hyperbolic arc segment of the cutting tip and the tangent point of the outer peripheral edge along the axis of the tool model. and Tangents With the edge line The included angle between them and the first rear angle of the bottom edge, From the start coordinates of the passivation point to the hyperbolic arc segment and tangent of the cutting edge Distance between tangent points To blunt the hyperbolic arc segment from the starting coordinates to the edge and the edge line The distance between the tangent points. Detailed Implementation
[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.
[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0020] Example: Please see Figures 1-5 The present invention provides a technical solution: A method for designing milling tools to suppress chatter, comprising the following steps: Step 1: Based on the diameter and shank length of the milling cutter to be produced, construct a cylindrical tool model. The tool model includes a shank part and a cutting edge part. On the cutting edge part, use the generatrix of the tool model as the path to perform scanning cut to obtain several peripheral cutting edges parallel to the generatrix of the tool model.
[0021] The specific method for scanning and cutting the cutting edge is as follows: determine the vertical center line of the milling cutter base, which is denoted as the generatrix of the tool model. Using the generatrix as the cutting path, scan and cut along the direction of the generatrix to form an even number of outer peripheral edges parallel to the generatrix of the milling cutter base, which are the cutting edges of the milling cutter. The outer peripheral cutting edge is generally selected with an even number of cutting edges, ranging from 2 to 6.
[0022] The specific steps for scanning and cutting are as follows: Using CAD software such as SolidWorks or AutoCAD, a 3D model of the tool is created. The model should include the tool holder and the cutting edge. The tool holder is typically a cylinder with a diameter equal to the diameter of the tool and a length equal to the length of the tool holder. The generatrix of the tool model is determined as the axis of the tool or the reference line for the cutting edge. A cutting path parallel to the generatrix of the tool model is drawn in the CAD software. A cross-sectional profile is created to represent the cutting edge of the tool. This profile should conform to the tool design and ensure consistency with the tool's functional requirements. The generatrix of the tool is selected as the path, and the previously defined cutting profile is selected as the section. The software will cut along the trajectory of the profile according to the generatrix, forming the outer peripheral cutting edge of the tool.
[0023] Step 2: Draw the chip groove structure based on the position of the outer peripheral cutting edge to form the corresponding bottom cutting edge of the tool. Connect the corresponding outer peripheral cutting edge and the bottom cutting edge of the tool with the hyperbolic arc segment of the tool tip. Determine the tangent points of the hyperbolic arc segment of the tool tip with the bottom cutting edge and the outer peripheral cutting edge respectively. Analyze the radial distance of the two tangent points along the radial direction of the tool model and the axial distance along the axial direction of the tool model. Construct the expression of the hyperbolic arc segment of the tool tip and transform it into the standard equation of the hyperbola through coordinate transformation.
[0024] The logic underlying the construction of the hyperbolic arc expression for the tool tip is as follows: A first coordinate system is constructed with the tool tip vertex as the origin. The bottom and outer cutting edges of the tool corresponding to that vertex are determined. The coordinates of the tangent points between the hyperbolic arc segment of the tool tip and the bottom and outer cutting edges are determined respectively. The tangent point between the hyperbolic arc segment of the tool tip and the bottom cutting edge is denoted as tangent point A, with coordinates [missing information]. The point of tangency between the hyperbolic arc segment of the blade tip and the outer peripheral cutting edge is denoted as tangency point B, with coordinates as follows: ,in The diameter of the milling cutter to be manufactured. The radial distance between the hyperbolic arc segment of the tool tip and the point of tangency of the bottom cutting edge along the radial direction of the tool model. The distance between the hyperbolic arc segment of the tool tip and the tangent point of the outer peripheral edge along the axis of the tool model; For coordinates tangent to the positive semi-axis of the horizontal axis and the positive semi-axis of the vertical axis and The conic section, with its implicit function expression, is: In the formula, y and y' are the x and y coordinates of the hyperbola segment at the tip of the knife in the first coordinate system, respectively. Let be the shape parameters of the hyperbolic arc segment of the blade tip, where Use this implicit function expression as the initial expression for the hyperbola segment at the tip of the knife.
[0025] Conic sections are curves formed by the intersection of a plane and a cone, including ellipses, parabolas, and hyperbolas. Depending on the cutting method, conic sections can have different geometric properties; in this expression, shape parameters are introduced. and tangent parameters and To describe a specific hyperbola shape; It should be noted that hyperbolas are commonly used in high-speed cutting or the design of special tools because their edge shapes can provide excellent cutting performance. The shape of the tool tip is described using a hyperbola, thus allowing for the selection of appropriate parameters. The shape of the hyperbola is controlled by parameters, which control the degree of opening of the hyperbola. Specifically, The larger the value, the narrower the opening of the hyperbola, indicating that the cutting angle of the tool will become sharper, making it suitable for certain materials with high requirements for cutting angle.
[0026] Among them, shape parameters When a hyperbola is tangent to the coordinate axes, the shape parameters of the hyperbola are | |>1, but this solution will Limited to Within the specified range, to control the curve from protruding outwards, a reasonable hyperbolic rounding is performed; and These are the hyperbolic arc segment at the tool tip and the tangent points at the bottom and outer peripheral edges of the tool. These two parameters clearly define the spatial positioning of the hyperbolic arc segment at the tool tip and influence the cross-sectional shape of the tool. This implicit function, by combining the above factors, forms a comprehensive description of the tool shape, enabling it to effectively reflect the tool's geometric characteristics, material cutting requirements, and machining conditions during the design process. It can meet the diverse needs of practical applications and ensure the effectiveness of the tool. Hyperbolas, being non-uniform curvature structures, provide multiple paths for force transmission. When a force is applied to a point, it is not transmitted in a single direction, but effectively dispersed over a wider area, resulting in a more uniform distribution and greater overall structural stability. For example, the hyperbolic design of cooling towers utilizes a hyperbolic structure, avoiding instability caused by uniform curvature through varying curvature; its stability far surpasses that of spherical designs. Hyperbolic towers employ a hyperbolic shape design, providing excellent seismic resistance. Roofs using a hyperbolic structure effectively disperse wind and gravity. This invention uses a hyperbolic structure for the transition of the tool tip and cutting edge. Applying these characteristics of hyperbolas to the tool of this invention effectively disperses cutting forces, reduces stress concentration, and improves machining stability, thereby reducing chatter. The hyperbolic shape of aircraft wings also optimizes airflow distribution, reduces flow separation and eddy current generation, thus reducing aerodynamic load fluctuations. Applying this property to this invention allows for a more rational distribution of cutting fluid, more uniform heat dissipation during tool cutting, reduced cutting thermal effects, and a more stable cutting process.
[0027] The logic behind transforming it into the standard equation of a hyperbola through coordinate transformation is as follows: the origin of the first coordinate system is moved to... At this point, and by flipping the x-axis, we obtain the second coordinate system as follows: ,in Let x be the x-coordinate of the second coordinate system. Let be the ordinate of the second coordinate system, and the mapping relationship between the coordinates of the first coordinate system and the second coordinate system is as follows: , Then the coordinates of the tangent point A are The coordinates of the tangent point B are The hyperbolic arc segment of the blade tip is transitionally connected to tangent points A and B in the second coordinate system. Based on the initial expression of the hyperbolic arc segment of the blade tip, the expression of the hyperbolic arc segment of the blade tip in the second coordinate system is: Will , Substituting the values, we obtain the standard equation of the hyperbola for the arc segment of the hyperbola. The specific expression for the standard equation of the hyperbola for the arc segment of the hyperbola is as follows: The range of values for the abscissa in the standard equation of a hyperbola is defined as follows: The range of values for the ordinate is .
[0028] This equation describes a complete hyperbola, but this solution only requires a finite length, namely the finite length tangent to the bottom and outer edges. Therefore, the domain of the function is... The range is defined as .
[0029] The initial implicit function expression is quite complex and not easily used directly to analyze the geometric properties of hyperbolas. Through coordinate transformation, the coordinate system of the curve can be adjusted to a more suitable framework for analysis, namely the second coordinate system. The choice of the second coordinate system makes the expression and geometric properties of the hyperbola clearer, facilitating the study of the hyperbola's geometric properties. By transforming the coordinates, the tangent point is converted to a second coordinate system, making the coordinate definition of the tangent point more intuitive. For example, the tangent point... and tangent point In the new coordinate system, connect to the horizontal and vertical axes respectively; the blade tip design requires the hyperbola to be able to reach the tangent point. and A smooth transition connection is achieved. By transforming coordinates, the complex coordinate relationships in the initial expression are eliminated, making the connection process simpler and more intuitive.
[0030] Step 3: Based on the standard equation of a hyperbola, and with the radial and axial distances being equal as constraints, constrain the shape parameters of the hyperbola segment at the cutting edge, determine the range of shape parameters for the hyperbola segment at the cutting edge, and thus determine the specific shape of the hyperbola segment at the cutting edge.
[0031] The constraint that the radial distance and axial distance are the same is specifically expressed as follows: Using a symmetrical hyperbola for arc transitions, ,remember Given the tangent length, the expression for the standard equation of the hyperbola of the knife-tip hyperbola segment is transformed into: Simplified to: In the formula, The specific value depends on the diameter of the blade. The range of values is determined by the tangent length. The range of values for is substituted into the simplified expression of the standard hyperbola equation for the hyperbola segment at the blade tip to determine the shape parameters of the hyperbola segment at the blade tip. The range of values for .
[0032] in, and Specific numerical values cannot be given, but if , The larger the value of , the farther the curve is from the origin of the second coordinate system. Therefore, a symmetrical hyperbola is used for the arc transition, making... ; The results of milling cutters of different diameters Different values, generally speaking Typically, it's 5% to 20% of the blade diameter, larger ones... It can withstand higher cutting forces and is suitable for large feed rates and smaller feed rates. Values can improve surface quality, making it suitable for detailed machining. To improve surface quality, avoid leaving marks on the machined surface, and prevent chipping due to weakened tool tip strength, control is crucial. Between 8% and 10% of the blade diameter, specifically for a blade diameter of 15mm. The value should be controlled between 1.2 and 1.5. Substituting this into the simplified expression for the standard equation of the hyperbola, we can derive... The range is 4≤ ≤5.25.
[0033] Similarly, the same applies to the processing of several other hyperbolic arc segments at the blade tip.
[0034] Step 4: Using a hyperbolic linear structure, the bottom edge, outer peripheral edge, and connected tip hyperbolic arc segment of the tool are blunted. Specifically, the second shape parameters of the cutting edge hyperbolic arc segment are determined by combining the tangent parallel to the tool axis at the tip point and the edge line at the tip point in the first flank face of the bottom edge. The blunting process is completed by the cutting edge hyperbolic arc segment. The blunted outer peripheral edge is twisted to obtain a helical structure of several outer peripheral edges, thus completing the structural design of the milling tool.
[0035] The cutting edge of a cutting tool is not absolutely sharp. Theoretically, a perfectly sharp cutting edge has a radius close to zero, which can greatly reduce cutting force. However, at the atomic scale, there will be microscopic defects due to the discontinuity of the crystal structure, resulting in extremely low actual strength. It is prone to chipping or rolling. An excessively thin cutting edge will be subjected to high stress during cutting, which can easily cause local stress to exceed the material's strength limit, accelerating wear or fracture. Furthermore, the chipping process of the cutting edge will also affect the surface finish. Therefore, proper passivation can disperse stress, thereby extending tool life and improving the surface finish to a certain extent.
[0036] The specific steps for determining the hyperbolic arc segment of the cutting edge include: The logic of the passivation process is as follows: the point of the tool tip closest to the tool's bottom edge and the tool's rotation center is recorded as the passivation start point, and the point of connection between the end of the outer peripheral edge and the tool holder is recorded as the passivation end point; Determine the tangent line parallel to the tool axis through the tool tip point, based on the closest point between the tool's bottom edge and the tool's rotation center. The edge line of the first back face of the bottom edge passing through the tip of the blade. Tangent Parallel to the tool axis and along the edge line In a plane, the hyperbolic arc segment of the cutting edge is composed of a line that... and The cross section formed by the hyperbola tangent on both sides is formed by scanning removal. The entire path formed by the bottom edge of the tool, the hyperbola arc segment at the tip of the tool, and the outer peripheral edge is the passivation scanning removal path. Intersect the extension line of the chip groove edge with the tangent. The intersection point is taken as the origin of the coordinate system, and the direction away from the bottom edge of the tool is taken as the positive semi-axis. The tangent line and edge line Establish a third coordinate system within the first quadrant of the Cartesian coordinate system, and mark the coordinates of the blunting starting point in the third coordinate system as follows: This refers to the tip of the cutting edge closest to the center of the tool's rotation, which is also the point where the two lines tangent to the hyperbolic arc segment meet. and Let the intersection point be M, and H be the ordinate of the passivation starting point in the third coordinate system. Then the tangent line... The equation is expressed as: In the formula, for Tangent The x-coordinate in the third coordinate system; edge line The equation is expressed as: In the formula, For the edge line In the ordinate of the third coordinate system, Tangent With the edge line The angle between them.
[0037] edge line Slope and first back angle of the bottom edge Regarding the first rear angle of the bottom edge of the present invention Greater than 0, therefore In the coordinate system, the direction is obliquely downward, let the tangent line... and edge line The included angle between them is ,but The slope is specifically expressed as: Let C be the arc segment of the hyperbola at the cutting edge and the tangent. If the point of tangency is C, then the coordinates of the point of tangency C are set as follows: Let D be the arc segment of the hyperbola cutting edge and... The tangent point.
[0038] set up From intersection point M Along the tangent to point C distance, ;set up From intersection point M Along the edge to the point of tangency D The distance; in order to use the general quadratic equation, we need to normalize the equation so that its value represents the directed distance from the point to the line; Based on tangent and edge line The equation expression is given, and the equation expression is normalized. The normalized value represents the directed distance from the point to the line. The specific formula used for normalization is as follows: In the formula, Tangent The normalized value, For the edge line The normalized value; Because the hyperbolic arc segment of the cutting edge is located on the edge line Below, therefore in order to The value is positive in the region where the hyperbolic arc segment of the cutting edge is located, therefore To take a negative value, the expression is: .
[0039] Based on tangent and edge line Based on the normalized values and their respective tangent lengths, the general implicit function equation for the hyperbola segment of the cutting edge is constructed as follows: In the formula, To blunt the hyperbolic arc segment from the starting coordinates to the cutting edge and the tangent Distance between tangent points To blunt the hyperbolic arc segment from the starting coordinates to the edge and the edge line The distance between the points of tangency will affect the tangent line. and edge line Substituting the normalized value into the general implicit function equation of the hyperbolic arc segment of the cutting edge, we obtain the specific equation expression of the hyperbolic arc segment of the cutting edge: In the formula, The shape parameters of the hyperbolic arc segment of the cutting edge.
[0040] The hyperbolic arc segment of the cutting edge is located on the edge line. Below a straight line, the region below it is typically a region less than 0. To make... The value is positive in the region where the curve is located (representing distance), therefore Take its negative value, that is .
[0041] in These are the shape parameters of the hyperbolic arc segment of the cutting edge. , The larger the value, the sharper the hyperbolic arc of the cutting edge and the closer it is to the intersection point M.
[0042] To facilitate manufacturing and ensure even force distribution on the cutting tool, take And 3μm≤ ≤12μm, not exceeding the depth of the first flank face and the chip groove; H is related to the chip groove parameters, the farther the highest point of the chip groove is from the tool tip, the larger the value of H; It is a tangent. and edge line The angle between them With the first rear corner of the bottom edge Related to, among them .
[0043] Thus, the tool tip undergoes two hyperbolic arc segment treatments to form a shell-shaped hyperboloid. The connection between this hyperboloid and the rake face and the first flank face is also a hyperbolic arc segment connection, which can better disperse the cutting force when the tool is cutting. The hyperbolic shell can resist the deformation required for chatter and minimize chatter. This type of hyperbolic paraboloid shell is used in buildings for large-span structures due to its high rigidity.
[0044] The present invention also provides a chatter suppression milling tool, which is manufactured by performing the above-described chatter suppression milling tool design method.
[0045] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.
[0046] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.
[0047] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.
[0048] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.
Claims
1. A method for designing milling tools to suppress chatter, characterized in that, The specific steps include: Based on the diameter and shank length of the milling cutter to be produced, a cylindrical tool model is constructed. The tool model includes a shank part and a cutting edge part. In the cutting edge part, a scanning cut is performed along the generatrix of the tool model to obtain several peripheral cutting edges parallel to the generatrix of the tool model. The chip groove structure is drawn based on the position of the outer peripheral edge to form the corresponding bottom edge of the tool. The corresponding outer peripheral edge and the bottom edge of the tool are connected by the hyperbolic arc segment of the tool tip. The tangent points of the hyperbolic arc segment of the tool tip with the bottom edge and the outer peripheral edge are determined respectively. The radial distance of the two tangent points along the radial direction of the tool model and the axial distance along the axial direction of the tool model are analyzed. The expression of the hyperbolic arc segment of the tool tip is constructed and transformed into the standard equation of the hyperbola through coordinate transformation. Based on the standard equation of a hyperbola, and with the radial and axial distances being equal as constraints, the shape parameters of the hyperbola segment at the cutting edge are constrained to determine the range of shape parameters for the hyperbola segment at the cutting edge, thereby determining the specific shape of the hyperbola segment at the cutting edge. Using a hyperbolic linear structure, the bottom edge, outer peripheral edge, and connected tip hyperbolic arc segment of the tool are blunted. Specifically, the second shape parameters of the cutting edge hyperbolic arc segment are determined by combining the tangent parallel to the tool axis at the tip point and the edge line at the tip point in the first flank face of the bottom edge. The blunting process is completed through the cutting edge hyperbolic arc segment. The blunted outer peripheral edge is then twisted to obtain a helical structure of several outer peripheral edges, thereby completing the structural design of the milling tool.
2. The chatter suppression milling tool design method according to claim 1, characterized in that: The specific method for scanning and cutting the cutting edge is as follows: determine the vertical center line of the milling cutter base, which is denoted as the generatrix of the tool model. Using the generatrix as the cutting path, scan and cut along the direction of the generatrix to form an even number of outer peripheral edges parallel to the generatrix of the milling cutter base, which are the cutting edges of the milling cutter.
3. The chatter suppression milling tool design method according to claim 2, characterized in that: The logic underlying the construction of the hyperbolic arc expression for the tool tip is as follows: A first coordinate system is constructed with the tool tip vertex as the origin. The bottom and outer cutting edges of the tool corresponding to that vertex are determined. The coordinates of the tangent points between the hyperbolic arc segment of the tool tip and the bottom and outer cutting edges are determined respectively. The tangent point between the hyperbolic arc segment of the tool tip and the bottom cutting edge is denoted as tangent point A, with coordinates [missing information]. The point of tangency between the hyperbolic arc segment of the blade tip and the outer peripheral cutting edge is denoted as tangency point B, with coordinates as follows: ,in The diameter of the milling cutter to be manufactured. The radial distance between the hyperbolic arc segment of the tool tip and the point of tangency of the bottom cutting edge along the radial direction of the tool model. The distance between the hyperbolic arc segment of the tool tip and the tangent point of the outer peripheral edge along the axis of the tool model; For coordinates tangent to the positive semi-axis of the horizontal axis and the positive semi-axis of the vertical axis and The conic section, with its implicit function expression, is: In the formula, y and y' are the x and y coordinates of the hyperbola segment at the tip of the knife in the first coordinate system, respectively. Let be the shape parameters of the hyperbolic arc segment of the blade tip, where Use this implicit function expression as the initial expression for the hyperbola segment at the tip of the knife.
4. The chatter suppression milling tool design method according to claim 3, characterized in that: The logic behind transforming it into the standard equation of a hyperbola through coordinate transformation is as follows: the origin of the first coordinate system is moved to... At this point, and by flipping the x-axis, we obtain the second coordinate system as follows: ,in Let x be the x-coordinate of the second coordinate system. Let be the ordinate of the second coordinate system, and the mapping relationship between the coordinates of the first coordinate system and the second coordinate system is as follows: , Then the coordinates of the tangent point A are The coordinates of the tangent point B are The hyperbolic arc segment of the blade tip is transitionally connected to tangent points A and B in the second coordinate system. Based on the initial expression of the hyperbolic arc segment of the blade tip, the expression of the hyperbolic arc segment of the blade tip in the second coordinate system is: Will , Substituting the values, we obtain the standard equation of the hyperbola for the arc segment of the hyperbola. The specific expression for the standard equation of the hyperbola for the arc segment of the hyperbola is as follows: The range of values for the abscissa in the standard equation of a hyperbola is defined as follows: The range of values for the ordinate is .
5. The chatter suppression milling tool design method according to claim 4, characterized in that: The constraint that the radial distance and axial distance are the same is specifically expressed as follows: Using a symmetrical hyperbola for arc transitions, ,remember Given the tangent length, the expression for the standard equation of the hyperbola of the knife-tip hyperbola segment is transformed into: Simplified to: In the formula, The specific value depends on the diameter of the blade. The range of values is determined by the tangent length. The range of values for is substituted into the simplified expression of the standard hyperbola equation for the hyperbola segment to determine the shape parameters of the hyperbola segment at the knife tip. The range of values for .
6. The chatter suppression milling tool design method according to claim 2, characterized in that: The logic of passivation is as follows: the point where the tool tip is closest to the tool rotation center is recorded as the passivation start point, and the point where the end of the outer peripheral edge is closest to the tool holder is recorded as the passivation end point; Determine the tangent line parallel to the tool axis through the tool tip point, based on the closest point between the tool's bottom cutting edge and the tool's rotation center. The edge line of the first back face of the bottom edge passing through the tip of the blade. Tangent Parallel to the tool axis and along the edge line In a plane, the hyperbolic arc segment of the cutting edge is composed of a line that... and The cross section formed by the tangent hyperbola is formed by scanning removal. The entire path formed by the bottom edge of the tool, the hyperbola arc segment at the tip of the tool, and the outer peripheral edge is the passivation scanning removal path. Intersect the extension line of the chip groove edge with the tangent. The intersection point is taken as the origin of the coordinate system, and the direction away from the bottom edge of the tool is taken as the positive semi-axis. The tangent line and edge line Establish a third coordinate system within the first quadrant of the Cartesian coordinate system, and mark the coordinates of the blunting starting point in the third coordinate system as follows: H is the ordinate of the passivation starting point in the third coordinate system, then the tangent line... The equation is expressed as: In the formula, Tangent The x-coordinate in the third coordinate system; edge line The equation is expressed as: In the formula, For the edge line In the ordinate of the third coordinate system, Tangent With the edge line The angle between them.
7. The chatter suppression milling tool design method according to claim 6, characterized in that: Based on tangent and edge line The equation expression is given, and the equation expression is normalized. The normalized value represents the directed distance from the point to the line. The specific formula used for normalization is as follows: In the formula, Tangent The normalized value, For the edge line The normalized value; Because the hyperbolic arc segment of the cutting edge is located on the edge line Below, therefore in order to The value is positive in the region where the hyperbolic arc segment of the cutting edge is located, therefore To take a negative value, the expression is: .
8. The chatter suppression milling tool design method according to claim 7, characterized in that: Based on tangent and edge line Based on the normalized values and their respective tangent lengths, the general implicit function equation for the hyperbola segment of the cutting edge is constructed as follows: In the formula, To blunt the hyperbolic arc segment from the starting coordinates to the cutting edge and the tangent Distance between tangent points To blunt the hyperbolic arc segment from the starting coordinates to the edge and the edge line The distance between the points of tangency will affect the tangent line. and edge line Substituting the normalized value into the general implicit function equation of the hyperbolic arc segment of the cutting edge, we obtain the specific equation expression of the hyperbolic arc segment of the cutting edge: In the formula, The shape parameters of the hyperbolic arc segment of the cutting edge.
9. A chatter suppression milling tool, characterized in that: The chatter suppression milling tool described herein is manufactured by implementing the chatter suppression milling tool design method according to any one of claims 1-8.