Design method for balancing cutting force between cutting edges of symmetrical gradient end mill

Abstract

The invention provides a design method for balancing cutting force between cutting edges of a symmetrical gradually-changing end mill, and relates to the technical field of shape characteristics of milling cutters, through the design of the gradually-changing cutting edges, a truncated edge is evolved into a sharp shape, and multifunctionality from rough machining to finish machining is achieved; the gradual change characteristic remarkably improves the chip breaking effect in the cutting process, tool adhesion is effectively prevented, meanwhile, cutting chip breaking is promoted by thinning cutting chips and reducing the bending rigidity of the cutting chips, in addition, due to the symmetrical design of the odd number of cutting edges and the even number of cutting edges, cutting force is balanced, cutting loads are reduced, abrasion is reduced, and the service life of the tool is prolonged. Further, the machining stability is enhanced, and high-quality surface quality and machining precision are ensured; through deep analysis of cutting force and distribution thereof, vibration is effectively reduced through the design, the stability of the cutter is further improved, the service life of the cutter is further prolonged, meanwhile, the fracture state of cuttings is optimized, and the machining efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shape characteristics of milling cutters, in particular to a balanced edge gap cutting force design method for a symmetrical progressive end mill. BACKGROUND

[0002] Nickel-based superalloys are widely used in aerospace, energy and other fields, and have excellent high-temperature performance and thermal fatigue resistance. However, in traditional milling machining, due to the large cutting force, the chip is not easy to break, the long filament chip increases the tool stress and wear, the cutting is not stable, and the workpiece surface quality is poor. At present, high-hardness materials and coatings are commonly used to prolong tool life and improve wear resistance, but the tool structure design has not effectively reduced wear and improved chip breaking effect. Tool edge passivation can extend the life by 50%-400%, by eliminating micro-notches, making the edge smooth and durable, reducing edge collapse, and improving workpiece surface finish and cutting stability; In the prior art, a high-efficiency drum-shaped profiling end mill with publication number CN110695426A has a cutting part and a handle part. The cutting part is provided with a plurality of chip removal grooves extending spirally from the bottom end to the handle part. The face of each chip removal groove towards the cutting rotation direction is the rake face. The rake face intersects with the outer peripheral surface of the cutting part to form a cutting edge. The cutting edge is processed to have a wavy edge and is divided into a circumferential cutting edge and a ball head cutting edge. The circumferential cutting edge profile is composed of two symmetrical circular arcs. The bottom end cutting edge is a ball head cutting edge, and each edge angle is not equal. The face of the outer peripheral surface of the cutting part connected with the cutting edge is the first flank face. The first flank face extends from the bottom end of the cutting part to the handle part, and the chip removal grooves are spirally distributed thereon. The present application has the advantages of greatly improving the efficiency of semi-finishing and finishing of workpieces, being able to machine narrow workpieces, having high strength, and having long service life.

[0003] Although the prior art has made certain progress in the design and application of progressive end mills, there are still many deficiencies. The current progressive end mill design often only focuses on the progressive characteristics of a single cutting edge, ignoring the mechanical balance between adjacent edges. This leads to uneven distribution of cutting forces in actual cutting process, which easily causes vibration and accelerates tool wear. In addition, the existing design method lacks in-depth study of the interaction between each cutting edge in the cutting force analysis, and fails to fully consider the complex relationship between cutting load, vibration and wear. Due to the change of cutting edge shape, the cutting load is not evenly distributed, which affects the overall cutting performance and machining quality of the tool. More seriously, this design defect is more obvious when machining high-hardness materials, which may cause sudden failure of the tool and affect the reliability of the entire machining system.

[0004] The information disclosed in the background section above 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 method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill, so as 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 balanced cutting forces between the cutting edges of a symmetrical graduated end mill is applied to the cutting edges of the cutter head of the graduated end mill. The number of cutting edges on the graduated end mill is set to an even number, and all cutting edges are marked sequentially, with odd-numbered marks representing odd-numbered edges and even-numbered marks representing even-numbered edges. The method ensures that the graduated edge form is identical for every other cutting edge. Adjacent cutting edges are designed symmetrically, and their graduated edge forms change in opposite directions. Specific steps include: Step S1: Analyze the cutting force under the current cutting conditions using cutting simulation software to determine the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges, and then determine the gradient cutting edge form suitable for the current tool material. Step S2: Under the determined gradient cutting edge form, set the fluctuation range of the cutting edge width and angle respectively; With an odd number of cutting edges, based on the set width fluctuation range, the width of the odd-numbered cutting edges is set to gradually narrow from the front end to the rear end of the cutting edge; the length of the cutting edge is set to Ld. The width variation function of odd-numbered blades is set as follows: It represents the width corresponding to the i-th odd-numbered blade. It decreases as position x increases, where The initial width of the cutting edge is an odd number, k is the basic rate of change of width, and x represents any position in the length of the cutting edge. With an even number of cutting edges, based on the set width fluctuation range, the width of the even-numbered cutting edge gradually widens from the front end to the rear end of the cutting edge; The width variation function of even-numbered blades is set as follows: It represents the width corresponding to the j-th even-numbered blade. It increases with increasing position x, where The initial width of the cutting edge tip is an even number; Within the set angular fluctuation range, the angles of odd-numbered and even-numbered blades gradually increase; And set the angle change function as This indicates that the angle JD corresponding to the cutting edge increases with the increase of position x, where Jd is the initial angle of the cutting edge tip and k1 is the basic rate of change of angle. Set the basic rate of change of width for odd-numbered blades and even-numbered blades to be the same, and also set the basic rate of change of angle for odd-numbered blades and even-numbered blades to be the same. Step S3: Based on the current basic change rate of width and basic change rate of angle, collect the cutting load, cutting vibration and wear data per unit time of the current incremental end mill, analyze and process these data, and comprehensively generate a change rate adjustment index to provide adjustment strategies for the basic change rate of width and basic change rate of angle; Step S4: Based on the adjusted basic change rate of width and basic change rate of angle, finally determine the gradient cutting edge form suitable for the current tool head material.

[0007] Furthermore, the initial curve of the cutting edge is set as a sine curve. The leader line corresponding to the termination curve For curves ; Determine the helix of the cutting edge as The cutting edge is composed of a rake face S0, a first flank face S1, and a second flank face S2, and the intersection of the rake face S0 and the first flank face S1 forms the cutting tip. ; Define the length of the first flank face S1 as Two rays are obtained by intersecting the rake face S0 and the first flank face S1 with the horizontal section, and the angle bisector of these two rays is denoted as... Point with the tip of the knife Starting from the angle bisector, Determine point C above, and set the tip of the knife... The line segment between point C and point C is taken as and limit the line segment The length is , The range of values ​​is ; at the angle bisector Among several mutually perpendicular line segments, the line segment passing through point C is represented as the perpendicular line segment. Define the perpendicular segment at this point. At the initial moment, and defining the rake face S0 and... The intersection point is B.

[0008] Furthermore, define the curve Starting from point C, and... Another parallel spiral; Starting from point B, and... Parallel spirals; Starting from point B and located within the rake face S0, with... The time axis is a sine curve, which represents the time axis... Used as the independent variable of the function corresponding to the sine curve; The sine curve is A1 represents the amplitude. Angular frequency, For the timeline, For phase shift, is the intercept of the time axis of the sine curve on the Z-axis, deviating from the center line; where The range of values ​​for A1 is: ;in For line segments Length; The design process for a gradient cutting edge on the cutting edge is defined as follows: To sweep the line segment, and with and The two curves serve as guide lines for the sweep, and remain constant throughout the sweep process. and The two surfaces intersect perpendicularly in space to form a gradually changing curved surface, and this gradually changing curved surface is used to cut the cutting edge of the end mill, ultimately forming a gradually changing cutting edge on the cutting edge. The specific settings for the gradient cutting edge type are as follows: Based on the premise that the total number of cutting edges is even, adjacent cutting edges include odd-numbered edges and even-numbered edges. The sweeping starting point of odd-numbered edges is a sine function starting from 0°, and the sweeping starting point of even-numbered edges is a sine function starting from 180°. That is, the period phase angle of adjacent odd-numbered edges and even-numbered edges differs by 180°, and the gradient cutting edge forms between odd-numbered edges are the same, and the gradient cutting edge forms between even-numbered edges are the same. The starting point and the ending point of the cutting edge are respectively regarded as one end and the other end, where the starting point and the ending point are the front end and the rear end of the tool head, respectively. The cutting edge width is set to be narrower from one end of the cutting edge to the other when the number of odd numbers are set, and wider from one end of the cutting edge to the other when the number of even numbers are set, so as to achieve mutual balance of cutting forces.

[0009] Furthermore, the formation of the gradient cutting edge also includes: Determine the center point H of the cutting tool, and then align the center point H of the cutting tool with the tip point. The line connecting the two axes is taken as the X-axis, and the axis of the tool holder is taken as the Z-axis, denoted as HZ. The rake face S0 lies in the XHZ plane, i.e. Points A and B are both located in the XHZ plane. The range of values ​​is ; Passing point Draw the development line of the end mill helix Draw a line through point B and... Parallel lines, and use these parallel lines as the development line of another spiral. Starting from point B, Plot a sine curve on the time axis The equation of the sine curve is A2 represents the amplitude. The Z-intercept of the time axis of the sine curve deviates from the center line; the range of values ​​for A2 is also... ; Define the axis HZ of the tool holder as the center of rotation of the helix. For the point Starting from point HZ, the point obtained by translating a certain distance in a direction perpendicular to the tool holder axis HZ is defined as follows: For the point Starting from point H, the point is obtained by translating a certain distance along a direction perpendicular to the axis HZ of the tool holder. Let the parallelogram... side, The edges are respectively at radius. , radius is By winding the spiral around a cylinder, a sine curve is obtained. The curve obtained after winding is the guide line of the cutting edge during the sweeping process. And the guide line With guide line All are curves .

[0010] Furthermore, determining the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges, and thus determining the gradient cutting edge form suitable for the current tool material, specifically includes: In the cutting simulation software, specific cutting conditions are set, including the material properties of the incremental end mill, as well as the simulation numerical range of cutting speed, feed rate, and depth of cut. Import the 3D model of the gradient end mill into the cutting simulation software, and clearly mark the number and type of cutting edges; specifically, represent odd-numbered edges with i and even-numbered edges with j. Assuming the total number of cutting edges is even, preliminary settings are made for adjacent odd-numbered and even-numbered edges, specifically defining their initial curves. Spirals and terminal curves The range of numerical parameters; this range includes the values ​​of the starting angle, ending angle, radius of curvature, and variation range of the cutting edge; When running the cutting simulation software, the simulation results of cutting force data are recorded under different cutting conditions and different combinations of numerical parameters for the cutting edge, initial curve, helix, and termination curve. The cutting force data includes the average cutting force and the cutting force fluctuation rate. The simulation results corresponding to these cutting force data are recorded in the analysis and comparison table. Different cutting conditions include arbitrary combinations of values ​​within a defined simulation range for cutting speed, feed rate, and depth of cut; For different combinations of numerical parameters of initial curves, helices and termination curves, including any combination of the starting angle, ending angle, radius of curvature and variation range of the cutting edge; The recorded cutting force data were analyzed, and the fluctuation rate of cutting force under different cutting conditions was calculated using the following formula: ; in, It is the cutting force fluctuation rate, which indicates the degree of fluctuation of the cutting force; the smaller the value, the more stable the cutting force. It is the fluctuation range of the cutting force, which is obtained by calculating the difference between the maximum and minimum values ​​of the cutting force data; These are the maximum and minimum values ​​in the cutting force data, respectively. It is the average cutting force; It is the sample size. It is the first The cutting force value of the sample was measured. The current cutting conditions are matched and screened with the analysis and comparison table to obtain the corresponding screening set in the analysis and comparison table. The cutting force fluctuation rate values ​​under different combinations of numerical parameters of initial curve, helix and termination curve are compared row by row in the screening set first, and the combination with the lowest cutting force fluctuation rate is initially selected. If there are multiple combinations with the lowest cutting force fluctuation rate, the initial curve, helix, and termination curve with the lowest average cutting force are further identified as the optimal combination; and based on the determined optimal combination of initial curve, helix, and termination curve, the gradient cutting edge form suitable for the current tool material is finally determined.

[0011] Furthermore, under the determined gradient cutting edge form, the fluctuation range of width and angle is set for each cutting edge; the fluctuation range of width is set to [-q1, +q1], and the fluctuation range of angle is set to [-q2, +q2]. The formula for calculating q1 is defined as follows: ; in, It is the diameter of the cutting tool; It is the width fluctuation coefficient; The formula for calculating q2 is defined as follows: ; in, It is the basic cutting angle of the cutting edge; It is the angular fluctuation coefficient; QV, JV, and Qd are the cutting speed, feed rate, and depth of cut, respectively; M is a material constant, and f is a function established based on experimental data and empirical formulas.

[0012] Furthermore, a rate adjustment index is generated to provide an adjustment strategy for the basic rate of change of width and the basic rate of change of angle, specifically including: The formula for calculating the rate of change adjustment index is defined as follows: ; Wherein, RI is the rate of change adjustment index; It is the cutting load, which represents the force that the graduated end mill bears during the cutting process; It is cutting vibration, which refers to the relative motion between the incremental end mill and the workpiece during the cutting process; It is the wear amount per unit time, representing the wear volume of the incremental end mill per unit time; It is the average width of odd-numbered blades and even-numbered blades; JD is the cutting edge angle that increases with increasing position x; and Both JD and 'A' are non-zero positive numbers; These are the weighting coefficients of the corresponding parameters, and ; The standardized output value of the rate of change adjustment index RI is adjusted to the range of (0, 1) by scaling and offsetting, and the standardized rate of change adjustment index is denoted as . ; Then determine The value range of is (0,1); when A value close to 1 indicates low cutting efficiency, requiring adjustment of the width and angle base variation rates of the gradient end mill to improve performance. when A value close to 0 indicates high cutting efficiency, meaning the gradient end mill is set to its optimal state and is suitable for the current cutting conditions.

[0013] Furthermore, adjust the rate of change index. The value range is divided into the following three intervals, and the calculation formulas for the basic change rate of width and the basic change rate of angle are provided for each interval, as follows: The upper limit thresholds for cutting load, cutting vibration, and wear per unit time are set as follows: , , ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to values ​​of ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to . , and The above applies; and the values ​​of u1, u2, and u3 are all within the range (0.65, 0.85). The low-load conditions for setting cutting load, cutting vibration, and wear per unit time are: , and The values ​​of u4, u5, and u6 are all within the range (0.23, 0.45). Interval 1: In this interval, the values ​​of cutting load, cutting vibration, and wear per unit time are all taken under high load conditions. This indicates that the cutting capability of the gradient end mill is poor, and it is necessary to increase the basic rate of change of the cutting edge width to distribute the cutting load and increase the basic rate of change of the angle to reduce the cutting thickness. The basic width variation rate is: ; The basic rate of change of angle is: ; During this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is within the range [h1, h2]. Interval 2: In this intermediate range, the rate of change adjustment index indicates that the cutting performance of the incremental end mill gradually improves, and at most two of the values ​​of cutting load, cutting vibration, and wear per unit time are taken under high load conditions. Furthermore, it is necessary to increase the basic rate of change of the cutting edge width to distribute the cutting load; and to increase the basic rate of change of the angle to reduce the cutting thickness. The basic width variation rate is: ; The basic rate of change of angle is: ; During this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is within the range [h3, h4]. Interval 3: In this low range, the rate of change adjustment index is in good condition, and the cutting load, cutting vibration, and wear per unit time are all at low load values; at this time... ; The basic width variation rate is: ; The basic rate of change of angle is: ; The adjustment range of the basic change rate of width and the basic change rate of angle should be within the range [h5, h6]. Furthermore, the adjustment range values ​​corresponding to the intervals [h1, h2], [h3, h4] and [h5, h6] decrease sequentially.

[0014] Compared with the prior art, the beneficial effects of the present invention are: through the gradual transition of the cutting edge design, the edge evolves from a blunt edge to a sharp shape, realizing the versatility from roughing to finishing; this gradual characteristic significantly improves the chip breaking effect during the cutting process, effectively prevents tool adhesion, and promotes chip breakage by thinning the chip and reducing its bending stiffness, making it particularly suitable for difficult-to-machine materials such as nickel-based superalloys. Furthermore, the symmetrical design of odd and even cutting edges balances the cutting force, reduces cutting load, decreases wear, extends tool life, and thus enhances machining stability, ensuring high-quality surface finish and machining accuracy. Through in-depth analysis of cutting forces and their distribution, this design effectively reduces vibration, further improving tool stability and lifespan, while optimizing chip fracture and increasing machining efficiency. This innovation not only provides new ideas for the design of gradient end mills but also offers a practical solution to the cutting problems of difficult-to-machine materials. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This invention relates to a graduated cutting edge shape end mill; Figure 3 This is a top view along the axis from the tip of the knife; Figure 4 This is a schematic diagram of the main cutting path and auxiliary helix of the cutting edge; Figure 5 It is a sinusoidal oscillating process for the formation of the cutting edge of an end mill; Figure 6 A schematic diagram of the key curves after unfolding the spiral into a straight line; Figure 7 This is a 3D model mapping of a sinusoidal oscillating end mill.

[0016] In the diagram: 1. Tool holder; 2. Tool head; 3. Cutting edge; 4. Chip groove; 5. End edge; D: Tool holder diameter; S0: Rake face; S1: First flank face; S1: Length of the first flank face; S2: Length of the second flank face; : The angle bisector between the front and rear cutting faces; : The tip of a knife. Detailed Implementation

[0017] 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.

[0018] 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.

[0019] Example: Please see Figures 1 to 7 The present invention provides a technical solution: A method for designing balanced cutting forces between the cutting edges of a symmetrical graduated end mill is applied to the cutting edges 3 at the cutter head 2 of the graduated end mill. The number of cutting edges 3 on the graduated end mill is set to an even number, and all cutting edges 3 are marked sequentially, with odd-numbered marks indicating odd-numbered edges and even-numbered marks indicating even-numbered edges. It is ensured that the graduated edge form of every other cutting edge 3 is exactly the same. Adjacent cutting edges 3 adopt a symmetrical design, and the graduated edge forms change in opposite directions. Specific steps include: Step S1: Analyze the cutting force under the current cutting conditions using cutting simulation software to determine the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges 3, and then determine the gradient cutting edge form suitable for the current tool head material 2. Step S2: Under the determined gradient cutting edge form, set the fluctuation range of the width and angle of the cutting edge 3 respectively; With an odd number of cutting edges, based on the set width fluctuation range, the width of the odd-numbered cutting edge 3 is set to gradually narrow from the front end to the rear end of the cutting edge; the length of the cutting edge 3 is set to Ld. The width variation function of odd-numbered blades is set as follows: It represents the width corresponding to the i-th odd-numbered blade. It decreases as position x increases, where The initial width of the front end of the odd-numbered cutting edge 3 is given by , k is the basic rate of change of width, and x represents any position within the length of the cutting edge 3; x is used to describe the continuous position of the tool from the front end to the rear end. With an even number of cutting edges, based on the set width fluctuation range, the width of the even-numbered cutting edge 3 gradually widens from the front end of the cutting edge to the rear end; The width variation function of even-numbered blades is set as follows: It represents the width corresponding to the j-th even-numbered blade. It increases with increasing position x, where The initial width of the front end of the even-numbered cutting edge 3; Within the set angular fluctuation range, the angles of odd-numbered and even-numbered cutting edges gradually increase, causing the cutting edge 3 to change from a blunt edge to a sharp edge. And set the angle change function as This indicates that the angle JD corresponding to the cutting edge 3 increases with the increase of position x, where Jd is the initial angle of the front end of the cutting edge 3 and k1 is the basic rate of change of angle. Set the basic rate of change of width for odd-numbered blades and even-numbered blades to be the same, and also set the basic rate of change of angle for odd-numbered blades and even-numbered blades to be the same. Step S3: Based on the current basic change rate of width and basic change rate of angle, collect the cutting load, cutting vibration and wear data per unit time of the current incremental end mill, analyze and process these data, and comprehensively generate a change rate adjustment index to provide adjustment strategies for the basic change rate of width and basic change rate of angle; Step S4: Based on the adjusted basic change rate of width and basic change rate of angle, finally determine the gradient cutting edge form suitable for the current material of the cutter head 2.

[0020] To further explain, the graduated end mill includes a shank 1 and a cutter head 2 arranged axially on the shank 1. The cutter head 2 is provided with a cutting edge 3, and the initial curve of the cutting edge 3 is set as a sine curve. The leader line corresponding to the termination curve For curves The cutting edge 3 has a chip removal groove 4 on its front side, and the bottom of the cutter head 2 has an end blade 5, which is tangent to the cutting edge 3. The curve guiding the change of the cutting edge 3 is formed by connecting the fastest curve segment with a straight line segment and an arc segment; the fastest curve segment is located at both ends of the cutting edge 3, so that the change rate of the width of the cutting edge 3 is maximized, and a rapid transition to different cutting effects is achieved; the straight line segment and the arc segment are located between the fastest curve segment, and the change rate of the width of the cutting edge 3 gradually decreases, so as to achieve a smooth change in cutting effect; The cutting edge 3 is composed of a rake face S0, a first flank face S1, and a second flank face S2, and the intersection of the rake face S0 and the first flank face S1 forms the cutting tip. , With the tip of the knife Starting from the same direction as the helix, and determined by the intersection of the rake face S0 and the first flank face S1; Define the length of the first flank face S1 as Two rays are obtained by intersecting the rake face S0 and the first flank face S1 with the horizontal section, and the angle bisector of these two rays is denoted as... Point with the tip of the knife Starting from the angle bisector, Determine point C above, and set the tip of the knife... The line segment between point C and point C is taken as and limit the line segment The length is , The range of values ​​is ; at the angle bisector Among several mutually perpendicular line segments, the line segment passing through point C is represented as the perpendicular line segment. Define the perpendicular segment at this point. The initial cutting position is defined as the vertical segment of the initial horizontal cross-section of the tool tip. Let S be the initial cutting position, and define the rake face S0 and... The intersection point is B.

[0021] For further explanation, please refer to [link / reference]. Figure 4 Define curve Starting from point C, and... Another parallel spiral; It is the main cutting path of the cutting edge, which directly affects the cutting performance; As an auxiliary spiral to the parallel lines, it helps maintain the geometry and cutting angle of the gradient end mill during cutting. Starting from point B, and... Parallel spirals; and by Figure 4 The location of point B is known. Located within the rake face S0; Starting from point B and located within the rake face S0, with... The time axis is a sine curve, which represents the time axis... Used as the independent variable of the function corresponding to the sine curve; The sine curve is A1 represents the amplitude. Angular frequency, For the timeline, For phase shift, is the intercept of the time axis of the sine curve on the Z-axis, deviating from the center line; where The range of values ​​for A1 is: ;in For line segments Length; The design process for the gradient cutting edge on cutting edge 3 is defined as follows: To sweep the line segment, and with and The two curves serve as guide lines for the sweep, and remain constant throughout the sweep process. and The two surfaces intersect perpendicularly in space to form a gradually changing curved surface, and this gradually changing curved surface is used to cut the cutting edge 3 of the end mill, ultimately forming a gradually changing cutting edge on the cutting edge 3. The specific settings for the gradient cutting edge type are as follows: Based on the premise that the total number of cutting edges 3 is even, adjacent cutting edges 3 include odd-numbered edges and even-numbered edges. The sweeping starting point of odd-numbered edges is a sine function starting from 0°, and the sweeping starting point of even-numbered edges is a sine function starting from 180°. That is, the period phase angle of adjacent odd-numbered edges and even-numbered edges differs by 180°, and the gradient edge form between odd-numbered edges is the same, and the gradient edge form between even-numbered edges is the same. The starting point and ending point of the cutting edge 3 are respectively regarded as one end and the other end, where the starting point and the ending point are the front end and the rear end of the tool head 2, respectively. The width of the cutting edge 3 is set to gradually narrow from one end of the cutting edge to the other when the number of cutting edges is odd, and gradually widen from one end of the cutting edge to the other when the number of cutting edges is even, so as to achieve mutual balance of cutting forces and effectively reduce vibration during the cutting process.

[0022] To further explain, such as Figure 6 As shown, the formation of a gradient cutting edge also includes: Determine the center point H of the cutter head 2, and align the center point H of the cutter head with the tip point. The line connecting the two axes is taken as the X-axis, and the axis of tool holder 1 is taken as the Z-axis, denoted as HZ. With the XHZ plane facing forward, the rake face S0 lies within the XHZ plane. Points A and B are both located in the XHZ plane. The range of values ​​is ; Passing point Draw the development line of a conventional end mill helix The development line of the helix of an end mill is the ray obtained by taking the tip of the end mill as the starting point and the helix angle as the development angle. It is drawn through point B. Parallel lines, and use these parallel lines as the development line of another spiral. Starting from point B, Plot a sine curve on the time axis The equation of the sine curve is A2 represents the amplitude; the range of values ​​for A2 is also [missing information]. ; Define the axis HZ of the tool holder as the center of rotation of the helix. For the point Starting from point HZ, the point obtained by translating a certain distance in a direction perpendicular to the tool holder axis HZ is defined as follows: For the point Starting from point H, the point is obtained by translating a certain distance along a direction perpendicular to the axis HZ of the tool holder. Let the parallelogram... side, The edges are respectively at radius. , radius is By winding the spiral around a cylinder, a sine curve is obtained. The curve obtained after winding is the guide line of the cutting edge 3 during the sweeping process. And the guide line With guide line All are curves .

[0023] In this embodiment, the shape of the cutting edge 3 is gradually changing. From one end of the cutting edge 3 to the other end, the shape, angle and width of the cutting edge 3 change accordingly. The width of the cutting edge 3 gradually narrows, so that the cutting edge 3 changes from wide to narrow, realizing the transition from thick to thin. The angle of the cutting edge 3 gradually increases, so that the cutting edge 3 changes from a blunt edge to a sharp edge. The shape of the cutting edge 3 gradually changes from blunt to sharp, achieving a smooth evolution of the cutting edge 3 shape. This gradual change in the shape of the cutting edge 3 gives the gradient end mill a versatility from roughing to finishing. The gradual cutting edge 3 helps improve chip breaking during the cutting process and prevents the gradient end mill from sticking. The gradual change in the shape of the cutting edge 3 provides a comprehensive solution for the gradient end mill with excellent cutting performance and wide adaptability. In this embodiment, the gradual change in the shape of the cutting edge 3 can progressively thin the chip, reducing its bending stiffness and facilitating chip breakage. This significantly improves the problem of discontinuous chips in nickel-based superalloys. Furthermore, the gradual change in the shape of the cutting edge 3 reduces the load on each cutting edge 3, thereby reducing the cutting load on the graduated end mill, slowing down its wear, and improving tool life. The discontinuous chips generated by the gradual change in the shape of the cutting edge 3 facilitate chip removal and avoid the negative effects of chip accumulation. Discontinuous chips also reduce cutting vibration and improve the stability of the cutting process. Because the cutting process is smoother, the surface quality and machining accuracy of the workpiece can be improved.

[0024] In this embodiment, the incremental end mill has multiple cutting edges 3, labeled as odd-numbered and even-numbered cutting edges. The odd-numbered cutting edges have the same shape change; the even-numbered cutting edges 3 also have the same shape change. However, the shape changes of the odd-numbered and even-numbered cutting edges are opposite. This symmetrical and opposite design of the two cutting edges ensures that the width of the odd-numbered cutting edges gradually narrows from one end of the cutting edge to the other, while the width of the even-numbered cutting edges gradually widens from one end of the cutting edge to the other. This achieves a balance of cutting forces and effectively reduces vibration during the cutting process. In this embodiment, a design employing two symmetrical cutting edges with opposite shapes balances the cutting force, effectively reducing vibration during the cutting process. The involute shape of the cutting edge 3, transitioning from positive to negative, gradually thins the chip, promoting chip breakage and reducing the cutting load on each cutting edge 3. The opposite gradient of the two cutting edges balances the chip thickness, maintaining a more uniform chip load and preventing single-edge impact from excessive chip thickness. The balance of cutting forces and the uniformity of chip load significantly improve the stability of the cutting process. Smoother cutting results in better workpiece surface quality and precision. This double-edge involute design effectively utilizes the principles of symmetry and gradient, improving the machinability of nickel-based superalloys.

[0025] In this embodiment, by changing the shape of the cutting edge 3 on the graduated end mill, the contact area between the flank face and the rake face S0 of the graduated end mill, as well as the contact state between the graduated end mill and the chip, can be altered. This reduces friction between the graduated end mill and the workpiece, changes the contact state between the graduated end mill and the chip, and reduces the possibility of chip adhesion. Furthermore, because the cutting edge 3 adopts a graduated design, the contact area between a single cutting edge 3 and the chip can be gradually reduced. This provides excellent anti-sticking properties, directly reducing cutting resistance during the cutting process. Anti-sticking not only reduces the cutting load on the graduated end mill but also reduces chip accumulation and improves cutting stability. This is extremely beneficial for improving the cutting performance of difficult-to-machine materials such as nickel-based superalloys.

[0026] To further explain, determining the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges 3, and thus determining the gradient cutting edge form suitable for the current tool head 2 material, specifically includes: 1.1) Set specific cutting conditions in the cutting simulation software. The cutting conditions include the material properties of the incremental end mill, as well as the simulated numerical ranges of cutting speed, feed rate, and depth of cut. The material properties include hardness and toughness. The cutting simulation software used is DEFORM. Based on the material properties of the gradient end mill, the following specific cutting conditions are set in the cutting simulation software: Based on expert group system or experimental data, the benchmark values ​​for cutting speed, feed rate and depth of cut are denoted as QV, JV and Qd, respectively. The cutting speed range is set to [QV×0.95, QV×1.05]; in this embodiment, QV=300mm / min is set, and the cutting speed range is 285mm / min to 315mm / min. The feed rate range is set to [JV×0.97, JV×1.03]; in this embodiment, JV is set to 0.15 mm / rev; the feed rate range is 0.145 mm / rev to 0.155 mm / rev. The cutting depth range is set to [Qd×0.9, Qd×1.1]; in this embodiment, Qd=2.0mm; the cutting depth range is 1.8mm to 2.2mm. The percentages in the above ranges are adjusted based on experimental data by the expert panel and are not limited thereto; Judgment criteria: After setting the above parameters, perform preliminary simulation to verify whether the cutting effect meets the requirements of the target cutting force. The target cutting force should be controlled within the rated range, with an allowable error of ±5%.

[0027] 1.2) Import the 3D model of the gradient end mill into the cutting simulation software, and clearly mark the number and type of the cutting edge 3; specifically, use i to represent odd-numbered edges and j to represent even-numbered edges; Ensure the tool geometry is detailed and accurate in order to perform precise cutting force analysis; The number of cutting edges 3 is set to 8; each cutting edge 3 is marked according to odd and even numbers to ensure that its number is even and to satisfy the symmetrical design of adjacent cutting edges.

[0028] 1.3) Based on the premise that the total number of cutting edges 3 is even, preliminary settings are made for adjacent odd-numbered and even-numbered edges, specifically defining their initial curves. Spirals and terminal curves The numerical parameter range includes the range of values ​​for the starting angle, ending angle, radius of curvature, and variation amplitude of the cutting edge; and the reference values ​​for the radius of curvature and variation amplitude are denoted as Qr and Bf, respectively. The radius of curvature is estimated using an empirical formula, specifically: ; in, It is the diameter of the gradient end mill. These are constants determined based on material and process characteristics. ; The specific values ​​were determined by the expert group based on experimental data and will not be elaborated further; the range of the radius of curvature was set as [Qr1, Qr2]; The magnitude of the change is estimated using the following formula: ; Wherein, Bf is the variation range, which is determined based on the material properties and the geometric characteristics of the gradient end mill, and its value range is between 0.1 and 1.0; Qd is the depth of cut, and JV is the feed rate; the value range of Bf is determined based on the numerical range of the depth of cut and the feed rate, and the value range of Bf is set as [Bf1, Bf2]. The larger the value of Qd, the more material is removed during the cutting of the gradient end mill, the greater the variation range, and thus the more cutting force and heat are generated; The higher the JV value, the higher the cutting speed of the gradient end mill, and the greater the variation range. It is necessary to maintain a stable cutting state and avoid tool overheating. Set the range of the starting angle to [0°, 180°]; Set the range of the ending angle to [0°, 180°]; Set the range of the radius of curvature to [Qr1, Qr2]; Set the range of values ​​for the change amplitude to [Bf1, Bf2]; Interaction rule: If the starting angle increases by 1°, the ending angle should decrease accordingly to maintain the overall shape of the cutting edge.

[0029] Set the main cutting path of the cutting edge to the corresponding helix. and set with the spiral The corresponding auxiliary spiral is To ensure that it maintains uniform contact and cutting effect during the cutting process; 1.4) When running the cutting simulation software, record the simulation results of cutting force data of cutting edge 3 under different cutting conditions and different combinations of numerical parameters of initial curve, helix and termination curve; the cutting force data includes average cutting force and cutting force fluctuation rate; and record the simulation results corresponding to these cutting force data in the analysis and comparison table; pay special attention to the difference in cutting force between adjacent cutting edges and its influence; Different cutting conditions include arbitrary combinations of values ​​within a defined simulation range for cutting speed, feed rate, and depth of cut; For different combinations of numerical parameters of initial curves, helices and termination curves, including any combination of the starting angle, ending angle, radius of curvature and variation range of the cutting edge 3; Using cutting simulation software, input each combination of initial and final curves one by one, and implement the cutting simulation process; The recorded cutting force data were analyzed, and the fluctuation rate of cutting force under different cutting conditions was calculated using the following formula: ; in, It is the cutting force fluctuation rate, which indicates the degree of fluctuation of the cutting force; the smaller the value, the more stable the cutting force. It is the fluctuation range of the cutting force, which is obtained by calculating the difference between the maximum and minimum values ​​of the cutting force data; These are the maximum and minimum values ​​in the cutting force data, respectively. It is the average cutting force; it represents the average cutting force under given cutting conditions. It is the sample size. It is the first The cutting force value of the sample was measured. 1.5) Match and filter the current cutting conditions with the analysis and comparison table to obtain the corresponding filter set in the analysis and comparison table. In the filter set, prioritize comparing the cutting force fluctuation rate values ​​under different combinations of numerical parameters of initial curves, helices and termination curves, and initially select the combination with the lowest cutting force fluctuation rate. If there are multiple combinations with the lowest cutting force fluctuation rate, then the initial curve, helix, and termination curve with the lowest average cutting force are further identified as the optimal combination. This combination not only exhibits the lowest cutting force fluctuation rate but also ensures the stability of cutting efficiency. Based on the determined optimal combination of initial curve, helix, and termination curve, the gradient cutting edge form suitable for the current tool head material is determined.

[0030] To further explain, under the determined gradient cutting edge form, the fluctuation range of width and angle is set for each cutting edge 3; the fluctuation range of width is set to ±q1, and the fluctuation range of angle is set to ±q2. The formula for calculating q1 is defined as follows: ; in, It is the diameter of the cutting tool; It is the width fluctuation coefficient; determined experimentally or empirically, and varies depending on the material and tool geometry; in this embodiment... ; The formula for calculating q2 is defined as follows: ; in, It is the basic cutting angle of cutting edge 3. It is the angular fluctuation coefficient; obtained through experiments or experience, reflecting the design and material properties of the cutting tool; in this embodiment... ; M is a material constant, and f is a function established based on experimental data and empirical formulas. It is determined through experimental verification. Tool design: Gradient end mills have different cutting edge geometries, so their width and angle will vary at different positions. Therefore, different tooling designs are needed based on the position of each specific cutting edge. and value; Machining conditions: Cutting speed, feed rate, and depth of cut affect the stability of width and angle, requiring adjustments. and The value should be adjusted accordingly; Experimental data: Conduct machining experiments and collect data in order to adjust and optimize the fluctuation range of width and angle to adapt it to specific cutting environments; In this embodiment, the width fluctuation range is [-0.1mm, +0.1mm], at which point q1=0.1mm, and the angle fluctuation range is [-2°, +2°], q2=2°; this is to ensure that it can adapt to changes in different gradient end mill materials and cutting conditions during actual machining; the values ​​of q1 and q2 are adjusted by the expert group based on experimental data and are not limited.

[0031] To further explain, the rate of change adjustment index, used to provide adjustment strategies for the basic rate of change of width and the basic rate of change of angle, specifically includes: The formula for calculating the rate of change adjustment index is defined as follows: ; Wherein, RI is the rate of change adjustment index; It is the cutting load, which represents the force that the graduated end mill bears during the cutting process; high cutting load will lead to accelerated wear of the graduated end mill. Cutting vibration (unit: m / s²) represents the relative motion between the end mill and the workpiece during the cutting process; vibration can lead to a decrease in machining accuracy. It is the wear amount per unit time (unit: mm³ / s), which represents the wear volume of the incremental end mill per unit time; excessive wear will shorten the life of the incremental end mill. It is the average width of the odd and even number of cutting edges; it affects the cutting performance of the gradient end mill. ; JD is the cutting edge angle that increases with position x; its change affects the cutting characteristics of the incremental end mill; and Both JD and 'A' are non-zero positive numbers; These are the weighting coefficients of the corresponding parameters, and ; The standardized output value of the rate of change adjustment index RI is adjusted to the range of (0, 1) by scaling and offsetting, and the standardized rate of change adjustment index is denoted as . ; ; in, This represents the minimum value of the original RI. This represents the maximum value of the original RI; Then determine The value range of is (0,1); when A value close to 1 indicates low cutting efficiency, requiring adjustment of the width and angle base variation rates of the gradient end mill to improve performance. when A value close to 0 indicates high cutting efficiency, meaning the gradient end mill is set to its optimal state and is suitable for the current cutting conditions.

[0032] It needs to be determined that the design of the cutting edge 3 should avoid =0 or JD=0.

[0033] To further explain, the rate of change is adjusted for the index. The value range is divided into the following three intervals, and the calculation formulas for the basic change rate of width and the basic change rate of angle are provided for each interval, as follows: Based on experimental verification, the upper limit thresholds for cutting load, cutting vibration, and wear per unit time were set as follows: , , ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to values ​​of ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to . , and The values ​​of u1, u2, and u3 are all within the range (0.65, 0.85); in this embodiment, u1, u2, and u3 are 0.66, 0.72, and 0.83, respectively. The low-load conditions for setting cutting load, cutting vibration, and wear per unit time are: , and The values ​​of u4, u5, and u6 are all within the range (0.23, 0.45); in this embodiment, u4, u5, and u6 are 0.24, 0.32, and 0.33, respectively. Interval 1: In this interval, the values ​​of cutting load, cutting vibration, and wear per unit time are all taken under high load conditions. This indicates that the cutting capability of the gradient end mill is poor; and it is necessary to increase the basic rate of change of the cutting edge width to distribute the cutting load, reduce the pressure per unit area, thereby reducing wear and increasing tool life; increasing the basic rate of change of the angle to reduce the cutting thickness is beneficial to chip flow. The basic width variation rate is: ; The basic rate of change of angle is: ; During this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is within the range [h1, h2], and the values ​​of h1 and h2 are within the range [20%, 28%]; in order to improve cutting characteristics and efficiency.

[0034] when In such cases, a comprehensive evaluation and re-optimization strategy for the gradient end mill design is recommended; when When the cutting efficiency is improved, it indicates that the cutting vibration and wear conditions still need to be monitored. Interval 2: In this intermediate range, the rate of change adjustment index indicates that the cutting performance of the incremental end mill gradually improves, and at most two of the values ​​of cutting load, cutting vibration, and wear per unit time are taken under high load conditions. ; The basic width variation rate is: ; The basic rate of change of angle is: ; At this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is in the range [h3, h4], and the values ​​of h3 and h4 are in the range [15%, 20%]. The strategy adjustment in this range will help improve cutting efficiency and the stability of the gradient end mill. Interval 3: In this low range, the rate of change adjustment index is in good condition, and the cutting load, cutting vibration, and wear per unit time are all at low load values; at this time... ; The basic width variation rate is: ; The basic rate of change of angle is: ; In this case, the cutting load Above 30N, cutting vibration Wear rate per unit time below 3m / s² Reduce to below 0.2 mm³ / s; the adjustment range of the basic change rate of width and the basic change rate of angle should be within the range [h5, h6], the value range of h5 and h6 is within the range of [5%, 20%], and the adjustment range values ​​corresponding to the intervals [h1, h2], [h3, h4] and [h5, h6] decrease sequentially.

[0035] Where h1 and h2 are the lower and upper limits of the adjustment range of the basic change rate of width and the basic change rate of angle in interval one, respectively; h3 and h4 are the lower and upper limits of the adjustment range of the basic change rate of width and the basic change rate of angle in interval two, respectively; h5 and h6 are the lower and upper limits of the adjustment range of the basic change rate of width and the basic change rate of angle in interval three, respectively; further, based on the adjusted basic change rate of width and the basic change rate of angle, the gradient cutting edge form applicable to the current material of the cutter head 2 is finally determined, specifically including: Given the optimal combination of the initial curve, helix, and termination curve, the gradient cutting edge form suitable for the current tool head material is obtained. The basic rate of change of width and the basic rate of change of angle, adjusted by the adjustment strategy, are defined as follows: ; where tz is an abbreviation for adjustment; Based on the adjusted basic rate of change of width and the basic rate of change of angle The established gradient cutting edge form will be adjusted, including the following: In gradient cutting edge design, the cutting edge width is optimized and adjusted according to a determined basic width variation rate; The angle of the cutting edge 3 is optimized according to the adjusted basic rate of change to ensure optimal cutting performance; Through the above adjustments, the final gradient cutting edge shape is formed, ensuring that it can achieve the expected cutting efficiency and tool life in actual cutting processes.

[0036] The final gradient cutting edge design has the following advantages: Better cutting performance and improved surface finish: The sinusoidal cutting edge design provides a smoother cutting edge, making the cutting process smoother, reducing fluctuations in cutting forces, and thus improving the surface quality of the final workpiece. Compared to ordinary end mills, it effectively reduces vibration and noise during the cutting process. For example, during high-speed cutting, ordinary end mills may cause chatter marks on the machined surface due to vibration, while sinusoidal cutting edge end mills can maintain better surface quality.

[0037] Reduce operating power consumption and extend tool life: This special cutting edge shape results in a more uniform load distribution on the cutting edge, reducing the contact area with the workpiece, minimizing localized excessive wear, and lowering power consumption during operation. For example, when machining metal materials for extended periods, the cutting edge of a conventional milling cutter may wear out or even chip quickly, while a sinusoidal cutting edge milling cutter can maintain a longer service life under the same machining conditions.

[0038] Improve machining accuracy: Sine curve end mills offer better control over chip formation and removal during cutting, thereby improving machining accuracy and surface finish. For example, in precision mold manufacturing, ordinary end mills may not meet the required high precision, while sinusoidal curve end mills can satisfy stringent precision standards.

[0039] Enhanced heat dissipation: The curved cutting edge increases the contact area between the cutting edge and the air, which is beneficial for heat dissipation. During continuous machining, ordinary end mills may deform due to heat accumulation, affecting machining accuracy, while end mills with sinusoidal cutting edges can better address the heat generation problem.

[0040] Adaptable to complex working conditions: For materials with uneven hardness or containing impurities, a sinusoidal cutting edge can better adapt to the workpiece contour, giving the milling cutter greater adaptability and helping to maintain the integrity of the cutting tip. In contrast, ordinary milling cutters are prone to chipping or decreased machining quality in such situations.

[0041] 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.

[0042] 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.

[0043] 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 according to actual needs.

[0044] 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 balanced cutting forces between the cutting edges of a symmetrical incremental end mill, characterized in that, This method applies to the cutting edge of the upper cutting head of a graduated end mill. The number of cutting edges on the graduated end mill is set to an even number, and all cutting edges are marked in sequence. Odd-numbered marks indicate odd-numbered edges, and even-numbered marks indicate even-numbered edges. It also ensures that the graduated edge form of every other cutting edge is exactly the same. Adjacent cutting edges are designed symmetrically, and the gradient cutting edge forms change in opposite directions. The specific steps include: Step S1: Analyze the cutting force under the current cutting conditions using cutting simulation software to determine the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges, and then determine the gradient cutting edge form suitable for the current tool material. Step S2: Under the determined gradient cutting edge form, set the fluctuation range of the cutting edge width and angle respectively; With an odd number of cutting edges, based on the set width fluctuation range, the width of the odd-numbered cutting edges is set to gradually narrow from the front end to the rear end of the cutting edge; the length of the cutting edge is set to Ld. The width variation function of odd-numbered blades is set as follows: It represents the width corresponding to the i-th odd-numbered blade. It decreases as position x increases, where The initial width of the cutting edge is an odd number, k is the basic rate of change of width, and x represents any position in the length of the cutting edge. With an even number of cutting edges, based on the set width fluctuation range, the width of the even-numbered cutting edge gradually widens from the front end to the rear end of the cutting edge; The width variation function of even-numbered blades is set as follows: It represents the width corresponding to the j-th even-numbered blade. It increases with increasing position x, where The initial width of the cutting edge tip is an even number; Within the set angular fluctuation range, the angles of odd-numbered and even-numbered blades gradually increase; And set the angle change function as This indicates that the angle JD corresponding to the cutting edge increases with the increase of position x, where Jd is the initial angle of the cutting edge tip and k1 is the basic rate of change of angle. Set the basic rate of change of width for odd-numbered blades and even-numbered blades to be the same, and also set the basic rate of change of angle for odd-numbered blades and even-numbered blades to be the same. Step S3: Based on the current basic change rate of width and basic change rate of angle, collect the cutting load, cutting vibration and wear data per unit time of the current incremental end mill, analyze and process these data, and comprehensively generate a change rate adjustment index to provide adjustment strategies for the basic change rate of width and basic change rate of angle; Step S4: Based on the adjusted basic change rate of width and basic change rate of angle, finally determine the gradient cutting edge form suitable for the current tool head material.

2. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 1, characterized in that: The initial curve of the cutting edge is set as a sine curve. The guide line corresponding to the termination curve For curves ; Determine the helix of the cutting edge as The cutting edge is composed of a rake face (S0), a first flank face (S1), and a second flank face (S2), and the intersection of the rake face (S0) and the first flank face (S1) forms the cutting tip. ); Define the length of the first flank face (S1) as ( Two rays are obtained by intersecting the rake face (S0) and the first flank face (S1) with the horizontal section respectively, and the angle bisector of these two rays is denoted as ( ). ), with the tip of the knife ( Starting from the angle bisector ( ), at the angle bisector ( Determine point C on the blade tip ( ) and set the blade tip point ( The line segment between point C and point C is taken as and limit the line segment The length is , The range of values ​​is ; At the angle bisector ( Among several mutually perpendicular line segments, the line segment passing through point C is represented as the perpendicular line segment. Define the perpendicular segment at this point. At the initial moment, and defining the rake face (S0) and... The intersection point is B.

3. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 2, characterized in that: Define curve ( () is starting from point C and... Another parallel spiral; Starting from point B, and... Parallel spirals; Starting from point B and located within the rake face (S0), The time axis is a sine curve, which represents the time axis... Used as the independent variable of the function corresponding to the sine curve; The sine curve is A1 represents the amplitude. Angular frequency, For the timeline, For phase shift, is the intercept of the time axis of the sine curve on the Z-axis, deviating from the center line; where The range of values ​​for A1 is: ;in For line segments Length; The design process for a gradient cutting edge on the cutting edge is defined as follows: To sweep the line segment, and with and The two curves serve as guide lines for the sweep, and remain constant throughout the sweep process. and The two surfaces intersect perpendicularly in space to form a gradually changing curved surface, and this gradually changing curved surface is used to cut the cutting edge of the end mill, ultimately forming a gradually changing cutting edge on the cutting edge. The specific settings for the gradient cutting edge type are as follows: Based on the premise that the total number of cutting edges is even, adjacent cutting edges include odd-numbered edges and even-numbered edges. The sweeping starting point of odd-numbered edges is a sine function starting from 0°, and the sweeping starting point of even-numbered edges is a sine function starting from 180°. That is, the period phase angle of adjacent odd-numbered edges and even-numbered edges differs by 180°, and the gradient cutting edge forms between odd-numbered edges are the same, and the gradient cutting edge forms between even-numbered edges are the same. The starting point and the ending point of the cutting edge are respectively regarded as one end and the other end, where the starting point and the ending point are the front end and the rear end of the tool head, respectively. The cutting edge width is set to be narrower from one end of the cutting edge to the other when the number of odd numbers are set, and wider from one end of the cutting edge to the other when the number of even numbers are set, so as to achieve mutual balance of cutting forces.

4. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 3, characterized in that: The formation of a gradient cutting edge also includes: Determine the center point H of the cutting head, and align the center point H of the cutting head with the tip point ( The line connecting the two axes is taken as the X-axis, and the axis of the tool holder is taken as the Z-axis, which is denoted as HZ. The rake face (S0) lies in the XHZ plane, that is, ( Points A and B are both located in the XHZ plane. The range of values ​​is ; Passing point Draw the development line of the end mill helix Draw a line through point B and... Parallel lines, and use these parallel lines as the development line of another spiral. Starting from point B, Plot a sine curve on the time axis The equation of the sine curve is A2 represents the amplitude. The Z-intercept of the time axis of the sine curve deviates from the center line; the range of values ​​for A2 is also... ; Define the axis HZ of the tool holder (1) as the center of rotation of the helix, For the point Starting from point HZ, the point obtained by translating a certain distance in a direction perpendicular to the tool holder axis HZ is defined as follows: For the point Starting from point H, the point is obtained by translating a certain distance along a direction perpendicular to the axis HZ of the tool holder. Let the parallelogram... side, The edges are respectively at radius. , radius is By winding the spiral around a cylinder, a sine curve is obtained. The curve obtained after winding is the guide line of the cutting edge during the sweeping process. And the guide line With guide line All are curves .

5. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 4, characterized in that: The process of determining the optimal combination of the initial curve, helix, and termination curve of adjacent cutting edges, and thus determining the gradient cutting edge form suitable for the current tool material, specifically includes: In the cutting simulation software, specific cutting conditions are set, including the material properties of the incremental end mill, as well as the simulation numerical range of cutting speed, feed rate, and depth of cut. Import the 3D model of the gradient end mill into the cutting simulation software, and clearly mark the number and type of cutting edges; specifically, represent odd-numbered edges with i and even-numbered edges with j. Assuming the total number of cutting edges is even, preliminary settings are made for adjacent odd-numbered and even-numbered edges, specifically defining their initial curves. Spirals and terminal curves The range of numerical parameters; this range includes the values ​​of the starting angle, ending angle, radius of curvature, and variation range of the cutting edge; When running the cutting simulation software, the simulation results of cutting force data are recorded under different cutting conditions and different combinations of numerical parameters for the cutting edge, initial curve, helix, and termination curve. The cutting force data includes the average cutting force and the cutting force fluctuation rate. The simulation results corresponding to these cutting force data are recorded in the analysis and comparison table. Different cutting conditions include arbitrary combinations of values ​​within a defined simulation range for cutting speed, feed rate, and depth of cut; For different combinations of numerical parameters of initial curves, helices and termination curves, including any combination of the starting angle, ending angle, radius of curvature and variation range of the cutting edge; The recorded cutting force data were analyzed, and the fluctuation rate of cutting force under different cutting conditions was calculated using the following formula: ； in, It is the cutting force fluctuation rate, which indicates the degree of fluctuation of the cutting force; the smaller the value, the more stable the cutting force. It is the fluctuation range of the cutting force, which is obtained by calculating the difference between the maximum and minimum values ​​of the cutting force data; These are the maximum and minimum values ​​in the cutting force data, respectively. It is the average cutting force; It is the sample size. It is the first The cutting force value of the sample was measured. The current cutting conditions are matched and screened with the analysis and comparison table to obtain the corresponding screening set in the analysis and comparison table. The cutting force fluctuation rate values ​​under different combinations of numerical parameters of initial curve, helix and termination curve are compared row by row in the screening set first, and the combination with the lowest cutting force fluctuation rate is initially selected. If there are multiple combinations with the lowest cutting force fluctuation rate, the initial curve, helix, and termination curve with the lowest average cutting force are further identified as the optimal combination; and based on the determined optimal combination of initial curve, helix, and termination curve, the gradient cutting edge form suitable for the current tool material is finally determined.

6. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 5, characterized in that: Under a given gradient cutting edge configuration, the width and angle fluctuation ranges are set for each cutting edge; the width fluctuation range is set to [-q1, +q1], and the angle fluctuation range is set to [-q2, +q2]. The formula for calculating q1 is defined as follows: ； in, It is the diameter of the cutting tool; It is the width fluctuation coefficient; The formula for calculating q2 is defined as follows: ； in, It is the basic cutting angle of the cutting edge; It is the angular fluctuation coefficient; QV, JV, and Qd are the cutting speed, feed rate, and depth of cut, respectively; M is a material constant, and f is a function established based on experimental data and empirical formulas.

7. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 6, characterized in that: Generate a rate adjustment index to provide adjustment strategies for the basic rate of change of width and the basic rate of change of angle, specifically including: The formula for calculating the rate of change adjustment index is defined as follows: ； Wherein, RI is the rate of change adjustment index; It is the cutting load, which represents the force that the graduated end mill bears during the cutting process; It is cutting vibration, which refers to the relative motion between the incremental end mill and the workpiece during the cutting process; It is the wear amount per unit time, representing the wear volume of the incremental end mill per unit time; It is the average width of odd-numbered blades and even-numbered blades; JD is the cutting edge angle that increases with the position x; and Both JD and 'A' are non-zero positive numbers; These are the weighting coefficients of the corresponding parameters, and ; The standardized output value of the rate of change adjustment index RI is adjusted to the range of (0, 1) by scaling and offsetting, and the standardized rate of change adjustment index is denoted as . ; Then determine The value range of is (0,1); when A value close to 1 indicates low cutting efficiency, requiring adjustment of the width and angle base variation rates of the gradient end mill to improve performance. when A value close to 0 indicates high cutting efficiency, meaning the gradient end mill is set to its optimal state and is suitable for the current cutting conditions.

8. The method for designing balanced cutting forces between the cutting edges of a symmetrical gradient end mill according to claim 7, characterized in that: Adjust the rate of change index The value range is divided into the following three intervals, and the calculation formulas for the basic change rate of width and the basic change rate of angle are provided for each interval, as follows: The upper limit thresholds for cutting load, cutting vibration, and wear per unit time are set as follows: , , ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to values ​​of ; and set the high-load conditions for cutting load, cutting vibration, and wear per unit time to . , and The above applies; and the values ​​of u1, u2, and u3 are all within the range (0.65, 0.85). The low-load conditions for setting cutting load, cutting vibration, and wear per unit time are: , and The values ​​of u4, u5, and u6 are all within the range (0.23, 0.45). Interval 1: In this interval, the values ​​of cutting load, cutting vibration, and wear per unit time are all taken under high load conditions. This indicates that the tapered end mill has poor cutting capability. It is also necessary to increase the basic rate of change of the cutting edge width to distribute the cutting load; and to increase the basic rate of change of the angle to reduce the cutting thickness; The basic width variation rate is: ； The basic rate of change of angle is: ； During this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is within the range [h1, h2]. Where h1 and h2 are the lower and upper limits of the adjustment range of the basic change rate of width and the basic change rate of angle in interval one, respectively; Interval 2: In this intermediate range, the rate of change adjustment index indicates that the cutting performance of the incremental end mill gradually improves, and at most two of the values ​​of cutting load, cutting vibration, and wear per unit time are taken under high load conditions. Furthermore, it is necessary to increase the basic rate of change of the cutting edge width to distribute the cutting load; and to increase the basic rate of change of the angle to reduce the cutting thickness. The basic width variation rate is: ； The basic rate of change of angle is: ； During this stage, the adjustment range of the basic change rate of width and the basic change rate of angle is within the range [h3, h4]. Where h3 and h4 are the lower and upper limits of the adjustment range of the basic change rate of width and the basic change rate of angle in interval two, respectively; Interval 3: In this low range, the rate of change adjustment index is in good condition, and the cutting load, cutting vibration, and wear per unit time are all at low load values; at this time... ; The basic width variation rate is: ； The basic rate of change of angle is: ； The adjustment range of the basic change rate of width and the basic change rate of angle should be within the range [h5, h6]. Among them, h5 and h6 are the lower limit and upper limit of the adjustment range of the basic change rate of width and the basic change rate of angle in interval three, respectively; Furthermore, the adjustment range values ​​corresponding to the intervals [h1, h2], [h3, h4], and [h5, h6] decrease sequentially.

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