A design method of adaptive milling cutter with adjustable curvature

Abstract

The application provides a design method of an adaptive milling cutter with adjustable curvature, and relates to the technical field of cutter design and manufacturing. The application defines a cutter radius and a fillet radius, constructs a transition curve from a peripheral edge part to an end edge bottom part through a Bezier curve, establishes a cutter rectangular coordinate system, determines a Bezier curve parameter equation based on control point coordinates, calculates a curvature and a change rate, and then finds a control parameter combination that makes a target function value maximum by discretizing the control point coordinates, calculating the target function value and optimizing and solving, so as to realize accurate regulation and control of the cutter curvature, optimize a blade edge geometric shape, and improve the adaptability and cutting performance of the cutter under complex machining conditions.

Description

Technical Field

[0001] This invention relates to the field of cutting tool design and manufacturing technology, specifically to an adaptive milling cutter design method with adjustable curvature. Background Technology

[0002] In the field of tool design and manufacturing technology, end mills, as key machining tools, directly affect cutting performance, machining efficiency, and tool life through their cutting edge geometry. Especially in complex surface machining, high-speed cutting, and high-precision manufacturing, the curvature design of the tool transition region is crucial. Currently, common end mill cutting edge transitions often employ single or multiple fixed-radius arc connections. This method has limited design variables and makes it difficult to achieve continuous and smooth curvature control, resulting in a relatively rigid cutting edge geometry and abrupt or discontinuous curvature transitions. This design limitation easily leads to cutting force fluctuations, stress concentration, and increased vibration, thereby affecting the surface quality, tool durability, and machining stability, failing to fully meet the increasingly demanding requirements of modern manufacturing for efficient, precise, and adaptive machining.

[0003] While some existing technologies attempt to incorporate spline curves or higher-order curves into cutting edge design, they still lack systematic curvature quantification analysis and active control mechanisms. This makes it difficult to achieve precise optimization and dynamic adaptation of the cutting edge curvature. Especially when pursuing the comprehensive goals of stable cutting force distribution, stress dispersion, and smooth cutting edge transition, this limits the adaptability and stability of the tool under high-speed, high-precision machining conditions, affecting machining efficiency and process reliability. Therefore, there is an urgent need for a design method that can flexibly control the tool curvature to reduce cutting force fluctuations, optimize the smoothness of curvature changes at the tool tip, and balance cutting efficiency and tool durability to meet the growing demand for efficient and precise machining in modern manufacturing.

[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 an adaptive milling cutter design method with adjustable curvature to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An adaptive milling cutter design method with adjustable curvature, comprising the following steps:

[0008] S1: Define the tool radius as R, the radius of the fillet transitioning from the peripheral cutting edge to the bottom of the end cutting edge as r, take the point of tangency between the fillet and the generatrix of the peripheral cutting edge as the starting point of the Bézier curve, and the point of tangency between the fillet and the bottom of the end cutting edge as the ending point of the Bézier curve, set the control parameters and construct the Bézier curve based on the control parameters.

[0009] S2: Using the tool axis as the Z-axis, rotate the Bézier curve around the Z-axis to form a three-dimensional rotary surface. The three-dimensional rotary surface connects with the rotary surface of the peripheral cutting edge. The center of the connecting surface is taken as the origin of the coordinate system. The intersection of the bottom of the end cutting edge and the tool axis is taken as the tool tip. The direction of the tool tip perpendicular to the tool holder is taken as the positive direction of the Z-axis. The direction of the starting position of the cutting edge of the peripheral cutting edge is taken as the X-axis. The Y-axis direction is determined based on the right-hand rule to establish the tool rectangular coordinate system.

[0010] S3: Determine the parametric equation of the Bézier curve based on the control parameters, calculate the curvature of different points on the Bézier curve as the control parameters change, construct the curvature interpolation function, and calculate the rate of change of curvature at any point on the Bézier curve.

[0011] S4: Discretize the control parameters within their respective ranges and generate several combinations of control parameters. Calculate the objective function value that characterizes the curvature fluctuation of the Bézier curve under each combination of control parameters. Determine the combination of control parameters that minimizes the objective function value as the optimal solution for the control points of the Bézier curve.

[0012] Furthermore, the central angle of a rounded corner is The tool radius and the fillet radius satisfy The point of tangency between the fillet and the generatrix of the circumferential cutting edge is A, which is taken as the starting point of the Bézier curve; the point of tangency between the fillet and the bottom of the end cutting edge is B, which is taken as the ending point of the Bézier curve; the vertical direction through A and the horizontal direction through B intersect at C. A moving point D is set on line segment AC, and a moving point E is set on line segment CB. D and E do not coincide with points A, B, and C, and the ordinate of D is -u, and the abscissa of E is v, where u represents the vertical descent rate control parameter, and v represents the horizontal extension control parameter. , ,in, This represents the minimum control parameter for u. This represents the maximum control parameter of u, and , , This represents the minimum control parameter for v. This represents the maximum control parameter for v, and , Using A, D, E, and B as control points, construct a Bézier curve.

[0013] Furthermore, the coordinates of each control point in the tool's rectangular coordinate system are: , , , The coordinates of the center of the rounded corner are .

[0014] Furthermore, the parametric equation of the Bézier curve is:

[0015]

[0016] in, Let represent the parameter variables of the Bézier curve, and , This indicates that the parameter variable on the Bézier curve is The coordinates of the points corresponding to the time are given, where A, B, D, and E represent the coordinates of each control point.

[0017] Set the x-coordinate corresponding to any parameter variable on the Bézier curve to . The vertical coordinate is set to The ordinate is 0. Calculate and The formula is:

[0018]

[0019] in, express x-coordinate express The vertical coordinate;

[0020] The formula used to calculate the curvature of different points on a Bézier curve as a function of u and v is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] in, Represents parameter variables The curvature at corresponding points express The first derivative, express The second derivative, express The first derivative, express The second derivative of .

[0027] Furthermore, the principle for calculating the rate of change of curvature at any point on a Bézier curve is as follows:

[0028] The range of values ​​for the parameter variable Discretize into several uniform points, with the parameter variables for each point as follows:

[0029]

[0030] in, Indicates the first The parameter variables at a uniform point The index of the uniform point, and , This indicates the number of uniform points within the range of values ​​for the parameter variable;

[0031] For each parameter variable, calculate its corresponding curvature to obtain a set of continuous data points. ,in, express Corresponding curvature:

[0032] based on and The constructed cubic polynomial is:

[0033]

[0034] in, express The corresponding curvature, These represent the constant coefficient, the linear coefficient, the quadratic coefficient, and the cubic coefficient, respectively.

[0035] The above formula is fitted using continuous data points to obtain... Differentiating the cubic polynomial yields the function of the rate of change of curvature: Substituting the parameter variables on the Bézier curve into the rate of curvature change function, we obtain the rate of curvature change at any point on the Bézier curve.

[0036] Furthermore, under the same combination of control parameters, any parameter variable Substituting into the curvature rate of change function, we obtain the curvature rate of change corresponding to the parameter variables: ,in, Indicates the combination of control parameters as At that time, parameter variables The corresponding rate of change of curvature is calculated for all parameters under the same combination of control parameters. The mean rate of change of curvature, based on different The objective function value is calculated using the rate of change of curvature and the mean rate of change of curvature, with the following formula:

[0037]

[0038]

[0039] in, Indicates all The mean rate of change of curvature, Indicates the combination of control parameters The corresponding objective function value;

[0040] exist and Within the range of values, and Each point is discretized into a grid of points, specifically in the following form:

[0041]

[0042]

[0043] in, express The discrete points, express The index of the discrete points, and , express The number of discrete points, express The discrete points, express The index of the discrete points, and , express The number of discrete points, generating J×L combination;

[0044] For each combination of control parameters Calculate its objective function value ;

[0045] The objective is to minimize the value of the objective function that reflects the curvature fluctuation of the Bézier curve, in all In the combination, find the one that makes The smallest group is denoted as Output the coordinates of the control point at this time. , .

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] This invention constructs the transition cutting edge line of a milling cutter from the circumferential cutting edge to the bottom of the end cutting edge using Bézier curves. Existing technologies typically use one or more fixed-radius arcs for connection. This method has few design variables, making it difficult to generate complex, non-circular, smooth transition shapes, and its curvature is relatively rigid and singular. This invention, however, uses third-order Bézier curves, generating several smoothly varying curve shapes through the coordinates of two moving points, ensuring the adjustment space for curvature. By calculating the curvature and the rate of change of curvature, precise quantification and active control of the micro-geometric properties of the cutting edge curve are achieved. The physical shape of the tool is transformed into a parametric equation, and spline interpolation is performed to cover all points within the value range. By solving the first and second derivatives at each point on the parametric equation, the curvature value at any point on the curve can be accurately calculated. Further calculation of the rate of change of curvature ensures a smooth transition of the cutting edge curvature, effectively dispersing stress, thereby improving tool life and cutting stability.

[0048] This invention also defines an objective function based on the standard deviation of the rate of curvature change and systematically finds the optimal solution using a global discretized grid search method. By minimizing the standard deviation of the rate of curvature change, it ensures that the cutting edge curve has a highly smooth curvature transition, avoiding sudden curvature changes in the cutting edge transition region. Control points are determined according to the optimization results, thereby determining the specific design parameters of the cutting edge. Compared with existing fixed-shape designs, this solution can generate optimal cutting edge curves for different working conditions, enabling the tool to adapt to specific machining requirements and ensuring that the machined cutting edge balances cutting efficiency and durability. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of the overall structure of the milling cutter according to an embodiment of the present invention;

[0051] Figure 3 This is a schematic diagram of the geometric structure of the end-edge fillet portion of the present invention.

[0052] right Figure 2 , Figure 3 Explanation: Figure 2 In the diagram, 1 represents the tool holder, 2 represents the tool axis, 1-1 represents the peripheral cutting edge, 1-2 represents the end-edge fillet cutting line, 1-3 represents the end-edge bottom, and X, Y, and Z represent the coordinate axes of the tool coordinate system. Indicates the origin of the tool coordinate system; Figure 3 In the center, O represents the center of the rounded corner, and its coordinates are... , Indicates the radius of the fillet. Indicates the tool radius. The central angle of the rounded corner, and , This indicates the point of tangency between the fillet and the generatrix of the circumferential cutting edge. This indicates the point of tangency between the fillet and the bottom of the end edge. Let A be the intersection of the vertical line segment passing through A and the horizontal line segment passing through B. Let D and E be moving points on line segments AC and BC that do not coincide with the endpoints, respectively. This represents a Bézier curve. Detailed Implementation

[0053] 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.

[0054] 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.

[0055] Example:

[0056] Please see Figures 1 to 3 The present invention provides a technical solution:

[0057] An adaptive milling cutter design method with adjustable curvature, comprising the following steps:

[0058] S1: Define the tool radius as R, the radius of the fillet transitioning from the peripheral cutting edge to the bottom of the end cutting edge as r, take the point of tangency between the fillet and the generatrix of the peripheral cutting edge as the starting point of the Bézier curve, and the point of tangency between the fillet and the bottom of the end cutting edge as the ending point of the Bézier curve, set the control parameters and construct the Bézier curve based on the control parameters.

[0059] In this embodiment, the central angle of the rounded corner is... The tool radius and the fillet radius satisfy The point of tangency between the fillet and the generatrix of the circumferential cutting edge is A, which is taken as the starting point of the Bézier curve; the point of tangency between the fillet and the bottom of the end cutting edge is B, which is taken as the ending point of the Bézier curve; the vertical direction through A and the horizontal direction through B intersect at C. A moving point D is set on line segment AC, and a moving point E is set on line segment CB. D and E do not coincide with points A, B, and C, and the ordinate of D is -u, and the abscissa of E is v, where u represents the vertical descent rate control parameter, and v represents the horizontal extension control parameter. , ,in, This represents the minimum control parameter for u. This represents the maximum control parameter of u, and , , This represents the minimum control parameter for v. This represents the maximum control parameter for v, and , Using A, D, E, and B as control points, construct a Bézier curve.

[0060] The milling cutter includes a shank portion 1 and a head portion. The head portion is composed of a peripheral cutting edge 1-1, a rounded end cutting edge 1-2, and a bottom end cutting edge 1-3. The peripheral cutting edge is located on the side of the cutter and provides the main cutting capability. The bottom end cutting edge is located at the bottom of the cutter. The rounded end cutting edge is located at the end of the cutter and is the transition area between the peripheral cutting edge and the bottom end cutting edge.

[0061] S2: Using the tool axis as the Z-axis, rotate the Bézier curve around the Z-axis to form a three-dimensional rotary surface. The three-dimensional rotary surface connects with the rotary surface of the peripheral cutting edge. The center of the connecting surface is taken as the origin of the coordinate system. The intersection of the bottom of the end cutting edge and the tool axis is taken as the tool tip. The direction of the tool tip perpendicular to the tool holder is taken as the positive direction of the Z-axis. The direction of the starting position of the cutting edge of the peripheral cutting edge is taken as the X-axis. The Y-axis direction is determined based on the right-hand rule to establish the tool rectangular coordinate system.

[0062] In this embodiment, the coordinates of each control point in the tool's rectangular coordinate system are: , , , The coordinates of the center of the rounded corner are .

[0063] By changing the coordinates of control points D and E through control parameters, the curvature of the milling cutter is altered. A vertical line is drawn through the starting point A, and a horizontal line is drawn through the ending point B. The intersection of the two lines is point C, and the coordinates of point C are... This generates a vertical line segment AC and a horizontal line segment BC. The Bézier curve is always tangent to line segments AC and BC. Simultaneously, line segments AC and BC are collinear at the perimeter and the bottom of the end edge, respectively. Therefore, the Bézier curve is tangent to both the perimeter and the bottom of the end edge, and the central angle... The range of values ​​for the fillet radius is: , At this extreme value, the shape of the end mill is similar to that of a ball end mill. If the value of u is too small, the smoothness and curvature continuity of the Bézier curve during transition cannot be fully utilized; D is a moving point located on the vertical line segment AC, with its x-coordinate being the fillet radius and its y-coordinate being -u, used to control the vertical descent rate of the Bézier curve. The larger the value of u, the closer point D is to point C. After leaving the starting point A, the Bézier curve will be strongly pulled towards point D, causing the Bézier curve to descend at a faster speed from the starting point, resulting in a more violent descent of the milling cutter, a steeper cutting edge shape, and a sharper tip. The smaller the value of u, the closer D is to the starting point A, and the weaker the downward pull on the Bézier curve after leaving the starting point A. Maintaining a longer horizontal trend with a slow descent results in a gentler vertical descent of the Bézier curve in the initial stage, with a flatter or rounded tip. E is a moving point on the horizontal line segment BC, with x-coordinate v and y-coordinate -r, used to control the horizontal extension speed of the Bézier curve. The larger the value of v, the closer E is to C, and the EB segment becomes longer and gentler, causing the Bézier curve to maintain a longer horizontal extension at the bottom before slowly turning towards the termination point B, with a gentler change in the horizontal direction. The smaller the value of v, the closer E is to point B, the shorter and steeper the EB segment becomes, and the curve leaves the horizontal extension state more quickly, with a faster horizontal extension speed.

[0064] S3: Determine the parametric equation of the Bézier curve based on the control parameters, calculate the curvature of different points on the Bézier curve as the control parameters change, construct the curvature interpolation function, and calculate the rate of change of curvature at any point on the Bézier curve.

[0065] In this embodiment, the parametric equation of the Bézier curve is:

[0066]

[0067] in, Let represent the parameter variables of the Bézier curve, and , This indicates that the parameter variable on the Bézier curve is The coordinates of the points corresponding to the time are given, where A, B, D, and E represent the coordinates of each control point.

[0068] The shape of a Bézier curve is determined by several control points. This scheme uses a third-order Bézier curve, which determines the curve shape through four control points. The coordinates of A and B are fixed as the starting and ending points, and the coordinates of the two control points D and E are changed by controlling the parameters u and v, thereby changing the curve shape. The parameter variable of the Bézier curve represents the position of a point on the curve, and its value range is... , The starting point corresponding to the Bézier curve, This corresponds to the endpoint of the Bézier curve; each term in the parametric equation of the Bézier curve contains a control point and a weighting function. As the starting point, when When the weight function is 1, it indicates that the Bézier curve starts from A; This is the first control term, used to control the initial direction of the curve after it leaves point A; This is the second control term, used to control the final direction of the curve before it approaches point B; For the termination term, when When the weight function is 1, it indicates that the Bézier curve ends at point B.

[0069] Set the x-coordinate corresponding to any parameter variable on the Bézier curve to . The vertical coordinate is set to The ordinate is 0. Calculate and The formula is:

[0070]

[0071] in, express x-coordinate express The vertical coordinate;

[0072] The formula used to calculate the curvature of different points on a Bézier curve as a function of u and v is:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] in, Represents parameter variables The curvature at corresponding points express The first derivative, express The second derivative, express The first derivative, express The second derivative of .

[0079] and The parametric equations of Bézier curves are decomposed into two axes, X and Z. Curvature represents the degree of bending of the cutting edge curve at different locations. In the calculation formula, the numerator is the magnitude of the curve's normal vector, reflecting the curvature of the curve, and the denominator is the cube of the magnitude of the tangent vector, used for normalization to make the curvature geometrically invariant. By adjusting the control parameters u and v, the cutting edge curvature distribution can be changed, thereby optimizing the cutting force distribution and reducing stress concentration.

[0080] The principle for calculating the rate of change of curvature at any point on a Bézier curve is as follows:

[0081] The range of values ​​for the parameter variable Discretize into several uniform points, with the parameter variables for each point as follows:

[0082]

[0083] in, Indicates the first The parameter variables at a uniform point The index of the uniform point, and , This indicates the number of uniform points within the range of values ​​for the parameter variable;

[0084] For each parameter variable, calculate its corresponding curvature to obtain a set of continuous data points. ,in, express Corresponding curvature:

[0085] based on and The constructed cubic polynomial is:

[0086]

[0087] in, express The corresponding curvature, These represent the constant coefficient, the linear coefficient, the quadratic coefficient, and the cubic coefficient, respectively.

[0088] The above formula is fitted using continuous data points to obtain... Differentiating the cubic polynomial yields the function of the rate of change of curvature: Substituting the parameter variables on the Bézier curve into the rate of curvature change function, we obtain the rate of curvature change at any point on the Bézier curve.

[0089] A finite number of discrete points on a Bézier curve can be calculated using the curvature formula. curvature value For discrete To find the derivative, first fit these discrete data points with a smooth function, then take the derivative of this smooth function; based on... and The correspondence is used to obtain continuous data points. This set of data points describes in The discrete relationship between curvature and parameter variables under the control parameter combination is analyzed. A cubic polynomial is chosen as the smoothing function to fit the discrete data points because it can describe the monotonic changes and extreme points of curvature, thus fully capturing the smooth trend of the blade curve curvature. Furthermore, cubic polynomials are less prone to overfitting and better reflect the overall trend rather than noise. The constructed cubic polynomial is as follows: Based on continuous data points, the least squares method is used for fitting to obtain... This leads to a smooth curvature function with t as the independent variable. Differentiating the curvature function yields the rate of change of curvature function. , to any parameter variable Substituting these values ​​into the rate of change of curvature function yields the parameter variables. The corresponding rate of change of curvature.

[0090] S4: Discretize the control parameters within their respective ranges and generate several combinations of control parameters. Calculate the objective function value that characterizes the curvature fluctuation of the Bézier curve under each combination of control parameters. Determine the combination of control parameters that minimizes the objective function value as the optimal solution for the control points of the Bézier curve.

[0091] In this embodiment, under the same combination of control parameters, any parameter variable Substituting into the curvature rate of change function, we obtain the curvature rate of change corresponding to the parameter variables: ,in, Indicates the combination of control parameters as At that time, parameter variables The corresponding rate of change of curvature is calculated for all parameters under the same combination of control parameters. The mean rate of change of curvature, based on different The objective function value is calculated using the rate of change of curvature and the mean rate of change of curvature, with the following formula:

[0092]

[0093]

[0094] in, Indicates all The mean rate of change of curvature, Indicates the combination of control parameters The corresponding objective function value;

[0095] Optimize u and v according to their value ranges under different machining scenarios to minimize the rate of curvature change within a given range, thereby achieving a balance of cutting forces. The objective function is the variance of the rate of curvature change. The rate of curvature change reflects the smoothness of the cutting edge. Curvature describes the degree of curvature bending, and the rate of curvature change describes the rate of curvature change. If the rate of curvature change fluctuates greatly, it indicates that the curvature of the cutting edge changes drastically at certain positions, which can easily lead to sudden changes in cutting forces and stress concentration. The objective function value reflects the volatility of curvature. The smaller the value, the more uniform the rate of change of curvature is distributed across the entire cutting edge, resulting in the smoothest geometry without obvious inflection points or abrupt changes. This helps to disperse cutting forces and reduce tool wear. The larger the objective function value, the more drastic the curvature change of the cutting edge, which may lead to geometrical abrupt changes and easily cause vibration or stress concentration. By minimizing the fluctuation of the rate of change of curvature, we can ensure that the cutting edge curve is as smooth as possible geometrically, thereby achieving a smooth transition of cutting forces and improving the adaptability and durability of the tool.

[0096] exist and Within the range of values, and Each point is discretized into a grid of points, specifically in the following form:

[0097]

[0098]

[0099] in, express The discrete points, express The index of the discrete points, and , express The number of discrete points, express The discrete points, express The index of the discrete points, and , express The number of discrete points, generating J×L combination;

[0100] For each combination of control parameters Calculate its objective function value ;

[0101] The objective is to minimize the value of the objective function that reflects the curvature fluctuation of the Bézier curve, in all In the combination, find the one that makes The smallest group is denoted as Output the coordinates of the control point at this time. , .

[0102] The range of values ​​for u is The range of values ​​for v is Discretize u and v into several points within their respective ranges, with J being the number of discrete points for u and L being the number of discrete points for v, and ensure that... , , , To cover the entire range of values, including all possible values. , A J×L grid matrix is ​​constructed, with a total of J×L combinations of control parameters; for each control parameter combination... Calculate all its discrete control parameters The rate of change of curvature is then calculated, along with the mean rate of change of curvature and the objective function value, under all control parameter combinations. Find the set of control parameters that minimizes the objective function value. This indicates that the blade curvature changes most smoothly at this point. Use this combination of control parameters as the actual control parameters and determine the coordinates of control points D and E based on the actual control parameters.

[0103] 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.

[0104] 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.

[0105] 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.

[0106] 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 an adaptive milling cutter with adjustable curvature, characterized in that, The specific steps include: S1: Define the tool radius as R, the radius of the fillet transitioning from the peripheral cutting edge to the bottom of the end cutting edge as r, take the point of tangency between the fillet and the generatrix of the peripheral cutting edge as the starting point of the Bézier curve, and the point of tangency between the fillet and the bottom of the end cutting edge as the ending point of the Bézier curve, set the control parameters and construct the Bézier curve based on the control parameters. S2: Using the tool axis as the Z-axis, rotate the Bézier curve around the Z-axis to form a three-dimensional rotary surface. The three-dimensional rotary surface connects with the rotary surface of the peripheral cutting edge. The center of the connecting surface is taken as the origin of the coordinate system. The intersection of the bottom of the end cutting edge and the tool axis is taken as the tool tip. The direction of the tool tip perpendicular to the tool holder is taken as the positive direction of the Z-axis. The direction of the starting position of the cutting edge of the peripheral cutting edge is taken as the X-axis. The Y-axis direction is determined based on the right-hand rule to establish the tool rectangular coordinate system. S3: Determine the parametric equation of the Bézier curve based on the control parameters, calculate the curvature of different points on the Bézier curve as the control parameters change, construct the curvature interpolation function, and calculate the rate of change of curvature at any point on the Bézier curve. S4: Discretize the control parameters within their respective ranges and generate several combinations of control parameters. Calculate the objective function value that characterizes the curvature fluctuation of the Bézier curve under each combination of control parameters. Determine the combination of control parameters that minimizes the objective function value as the optimal solution for the control points of the Bézier curve.

2. The adjustable curvature adaptive milling cutter design method according to claim 1, characterized in that: In S1, the central angle of the rounded corner is... The tool radius and the fillet radius satisfy The point of tangency between the fillet and the generatrix of the circumferential cutting edge is A, which is taken as the starting point of the Bézier curve; the point of tangency between the fillet and the bottom of the end cutting edge is B, which is taken as the ending point of the Bézier curve; the vertical direction through A and the horizontal direction through B intersect at C. A moving point D is set on line segment AC, and a moving point E is set on line segment CB. D and E do not coincide with points A, B, and C, and the ordinate of D is -u, and the abscissa of E is v, where u represents the vertical descent rate control parameter, and v represents the horizontal extension control parameter. , ,in, This represents the minimum control parameter for u. This represents the maximum control parameter of u, and , , This represents the minimum control parameter for v. This represents the maximum control parameter for v, and , Using A, D, E, and B as control points, construct a Bézier curve.

3. The adaptive milling cutter design method with adjustable curvature according to claim 2, characterized in that: The coordinates of each control point in the tool's rectangular coordinate system are: , , , The coordinates of the center of the rounded corner are .

4. The adaptive milling cutter design method with adjustable curvature according to claim 3, characterized in that: The parametric equation of the Bézier curve in S3 is: in, Let represent the parameter variables of the Bézier curve, and , This indicates that the parameter variable on the Bézier curve is The coordinates of the points corresponding to the time are given, where A, B, D, and E represent the coordinates of each control point. Set the x-coordinate corresponding to any parameter variable on the Bézier curve to . The vertical coordinate is set to The ordinate is 0. Calculate and The formula is: in, express x-coordinate express The vertical coordinate; The formula used to calculate the curvature of different points on a Bézier curve as a function of u and v is: in, Represents parameter variables The curvature at corresponding points express The first derivative, express The second derivative, express The first derivative, express The second derivative of .

5. The adaptive milling cutter design method with adjustable curvature according to claim 4, characterized in that: The principle for calculating the rate of change of curvature at any point on the Bézier curve in S3 is as follows: The range of values ​​for the parameter variable Discretize into several uniform points, with the parameter variables for each point as follows: in, Indicates the first The parameter variables at a uniform point The index of the uniform point, and , This indicates the number of uniform points within the range of values ​​for the parameter variable; For each parameter variable, calculate its corresponding curvature to obtain a set of continuous data points. ,in, express Corresponding curvature: based on and The constructed cubic polynomial is: in, express The corresponding curvature, These represent the constant coefficient, the linear coefficient, the quadratic coefficient, and the cubic coefficient, respectively. The above formula is fitted using continuous data points to obtain... Differentiating the cubic polynomial yields the function of the rate of change of curvature: By substituting the parameter variables on the Bézier curve into the curvature change rate function, the curvature change rate at any point on the Bézier curve can be obtained.

6. The adaptive milling cutter design method with adjustable curvature according to claim 5, characterized in that: In S4, under the same combination of control parameters, any parameter variable Substituting into the curvature rate of change function, we obtain the curvature rate of change corresponding to the parameter variables: ,in, Indicates the combination of control parameters as At that time, parameter variables The corresponding rate of change of curvature is calculated for all parameters under the same combination of control parameters. The mean rate of change of curvature, based on different The objective function value is calculated using the rate of change of curvature and the mean rate of change of curvature, with the following formula: in, Indicates all The mean rate of change of curvature, Indicates the combination of control parameters The corresponding objective function value; exist and Within the range of values, and Each point is discretized into a grid of points, specifically in the following form: in, express The discrete points, express The index of the discrete points, and , express The number of discrete points, express The discrete points, express The index of the discrete points, and , express The number of discrete points, generating J×L combination; For each combination of control parameters Calculate its objective function value ; The objective is to minimize the value of the objective function that reflects the curvature fluctuation of the Bézier curve, in all In the combination, find the one that makes The smallest group is denoted as Output the coordinates of the control point at this time. , .

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