A milling cutter with star-shaped wire edge and an optimization method thereof

Abstract

The application discloses a milling cutter with star-shaped line cutting edges and an optimization method thereof, and relates to the technical field of milling cutter design, which comprises the following steps: determining the initial value of a scale factor based on production target parameters, adjusting the initial value in combination with the hardness value of a machining target material and cutting process parameters to obtain the accurate scale factor of a single star-shaped line cutting edge, constructing a milling cutter model, establishing a plane coordinate system at the center of a cutter head, determining the curvature of the star-shaped line according to a single star-shaped line cutting edge parameter equation containing the accurate scale factor and an angle change parameter, rotating the cutter head center by different angles to form a plurality of star-shaped line cutting edges with different positions, and respectively adopting a circular arc, a spline curve and a helical transition surface to optimize the transition connection between the sharp corners in the star-shaped line cutting edge, adjacent star-shaped line cutting edges and the star-shaped line cutting edge and the cylindrical surface of the cutter head, so as to help optimize the load distribution during cutting, reduce vibration and wear.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of milling cutter design, in particular to a milling cutter with a star-shaped line cutting edge and an optimization method thereof. BACKGROUND

[0002] In the field of mechanical processing, milling is widely used in the manufacturing of various parts. With the increasing demand for product precision and surface quality in the manufacturing industry, the traditional milling cutter cutting edge shape gradually exposes many limitations when machining complex-shaped workpieces or high-precision parts. The conventional straight line or simple curve cutting edge milling cutter has uneven cutting force distribution during cutting, which is prone to vibration, resulting in increased machining surface roughness, difficulty in ensuring dimensional accuracy, and faster tool wear and shorter tool life.

[0003] As a special geometric curve, the star-shaped line has unique shape characteristics, and its multiple sharp corners and smooth transition areas provide a new idea for milling cutter cutting edge design, and it can help optimize load distribution during cutting and reduce vibration and wear. However, there is currently no mature technology for applying star-shaped lines to milling cutter cutting edges, and there is a lack of systematic design methods and reasonable cutting edge transition forms for star-shaped line cutting edge milling cutters, which limits their application in actual production.

[0004] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The purpose of the present application is to provide a milling cutter with a star-shaped line cutting edge and an optimization method thereof to solve the problems raised in the background.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] A milling cutter with a star-shaped line cutting edge, specifically comprising:

[0008] The milling cutter includes a shank, a body and a head, the body is used to connect the shank and the head, the head has not less than 3 cutting edges designed based on the star-shaped line distributed on its circumference, a milling cutter model is constructed according to the structure of the milling cutter, the head part of the milling cutter model is determined, and a plane coordinate system is established with the center of the head as the coordinate origin, a single star-shaped line cutting edge parameter equation containing an accurate scale factor and an angle change parameter is determined, and the cutting edge determination method of the milling cutter is:

[0009] The initial value of the scale factor is determined based on the production target parameters, and the initial value of the scale factor is adjusted through the hardness value of the target material and the cutting process parameters to obtain the accurate scale factor of the single star-shaped line cutting edge;

[0010] The curvature of the star-shaped line is determined according to a single star-shaped line edge parameter equation, a plurality of star-shaped line edges are constructed, and the plurality of star-shaped line edges are respectively rotated by different angles around the center of the tool head, and finally a plurality of star-shaped line edges in different positions are formed.

[0011] The sharp corners of the star-shaped line edge, the adjacent star-shaped line edges, and the star-shaped line edge and the cylindrical surface of the tool head are respectively connected by a circular arc, a spline curve and a spiral transition surface, and the transition connection method is as follows:

[0012] The transition arc radius is determined by the cutting processing requirement, and the center position of the transition arc is determined based on the tangent line of the sharp corner of the star-shaped line, so as to determine the transition arc equation and realize the arc transition of the sharp corner of the star-shaped line edge.

[0013] On each star-shaped line edge, a plurality of turning key points are selected, and a continuous spline curve passing through all selected key points is constructed based on a cubic spline interpolation algorithm, so as to realize the transition connection of adjacent star-shaped line edges.

[0014] Based on the radius of the cylindrical surface of the tool head, the selected pitch and the geometric parameters of the spiral transition surface are combined to construct the spiral transition surface equation, so as to determine the spiral transition surface and realize the transition connection of the star-shaped line edge and the cylindrical surface of the tool head.

[0015] Further, the initial value of the scale factor is determined based on the production target parameters, including the diameter of the tool head and the number of edges, and the formula for calculating the initial value of the scale factor is:

[0016] ;

[0017] In the formula, is the initial value of the scale factor, is the diameter of the tool head, is the number of edges, and is an empirical coefficient, which is specifically set to , ;

[0018] The logic for adjusting the initial value of the scale factor by the hardness value of the target material and the cutting process parameters is that the cutting process parameters include the cutting speed setting target value and the cutting feed amount setting target value, and the adaptive adjustment factor is generated based on the cutting process parameters and the hardness value of the target material. The formula for calculating the adaptive adjustment factor is:

[0019] ;

[0020] In the formula, is the adaptive adjustment factor, a target value of hardness of the material to be processed, a reference value of hardness of the material to be processed, a target value of cutting speed, a reference value of cutting speed, a target value of cutting feed amount, a reference value of cutting feed amount, 、 and a weight coefficient, wherein and 、 and are all greater than 0;

[0021] The precise scale factor is specifically obtained by adaptive adjustment of the scale factor initial value, and the formula according to which the calculation is specifically made is:

[0022] ;

[0023] In the formula, the precise scale factor is taken as the scale factor of the single star-shaped line blade edge parameter equation.

[0024] Further, the XOY plane coordinate system flush with the horizontal cross section of the tool head is established with the center of the tool head as the coordinate origin, and the single star-shaped line blade edge parameter equation is specifically:

[0025] ;

[0026] In the formula, and are respectively the horizontal coordinate and the vertical coordinate of the plane coordinate system, is the angle change parameter of the star-shaped line, wherein .

[0027] Further, the formula according to which the curvature of the star-shaped line is determined according to the precise scale factor is:

[0028] ;

[0029] In the formula, is the curvature of the star-shaped line, is the first-order derivative of the horizontal coordinate of the star-shaped line with respect to the angle change parameter, is the first-order derivative of the vertical coordinate of the star-shaped line with respect to the angle change parameter, is the second-order derivative of the horizontal coordinate of the star-shaped line with respect to the angle change parameter, is the second-order derivative of the vertical coordinate of the star-shaped line with respect to the angle change parameter;

[0030] Derivation of the single star-shaped line blade parameter equation and substitution into the curvature formula of the star-shaped line to obtain the simplified formula of the curvature of the star-shaped line, as follows

[0031] ;

[0032] Where the maximum value of the curvature k takes , and the minimum value is 0;

[0033] Rotate a plurality of star-shaped line blades around the center of the tool head by different angles, and the curve equation after rotation is:

[0034] ;

[0035] In the formula, is the horizontal coordinate of the kth star-shaped line blade after rotation, is the vertical coordinate of the kth star-shaped line blade after rotation, is the rotation angle of the kth star-shaped line blade, and k is the index of the star-shaped line blade.

[0036] Further, the sharp corners of the star-shaped line blade are transitioned with a circular arc, and the logic for determining the specific transition circular arc radius is as follows: the cutting processing requirements include: target material hardness value, target cutting force setting value, target cutting speed setting value and target cutting depth setting value, based on the cutting processing requirements, combined with the tool head diameter parameter, the formula for determining the specific transition circular arc radius is:

[0037] ;

[0038] In the formula, is the transition circular arc radius, is the target cutting force setting value, is the target cutting depth setting value, is the maximum cutting force, is the maximum cutting speed, is the maximum cutting depth, is the maximum tool head diameter, , , and are weight coefficients, which are specifically set as , , , and are nonlinear exponents, ;

[0039] The logic for determining the position of the center of the transition arc is as follows: taking the tangent of the star-shaped line at the sharp corner as the reference, the center of the transition arc is located at a position perpendicular to the tangent and at a distance of the radius of the transition arc from the vertex of the sharp corner, and the arc equation is determined through the center and the radius, so as to transition the sharp corner of the blade edge of the star-shaped line.

[0040] Further, the logic for determining the spline curve for the transition connection of adjacent star-shaped line blade edges is as follows: a plurality of turning key points are systematically selected, the turning key points include the starting point and the ending point of the blade edge and a plurality of turning points in the region therebetween, the spline curve is determined based on the turning key points through a spline interpolation algorithm, and the calculation formula of the spline interpolation is as follows:

[0041] ;

[0042] In the formula, is a spline curve function, is a position argument of the spline curve, , , and are to-be-determined coefficients, the to-be-determined coefficients are determined through interpolation calculation by using a cubic spline interpolation formula, and the logic for determining the to-be-determined coefficients is as follows: a linear equation group is established based on the constraint conditions of the function value and the derivative value of the spline curve to solve the coefficients of the spline curve, and specifically, the to-be-determined coefficients are determined by taking the function value, the first-order derivative and the second-order derivative of the spline curve as periodic boundary conditions; wherein the periodic boundary conditions are specifically set as:

[0043] ;

[0044] In the formula, and are the starting point and the ending point of the spline curve respectively, and are the first-order derivative at the starting point and the ending point of the spline curve respectively, and are the second-order derivative at the starting point and the ending point of the spline curve respectively.

[0045] Further, the geometric parameters of the spiral transition surface specifically include the radius of the tool head cylindrical surface, the distance from the tool head center to the spiral transition surface, the angle parameter of the spiral line and the angle parameter of rotation around the tool head axis, and the specific equation of the spiral transition surface is as follows:

[0046] ;

[0047] In the formula, , and are the horizontal coordinate, the vertical coordinate and the vertical coordinate of the spiral transition surface respectively, is the radius of the tool head cylindrical surface, This is the distance from the center of the cutter head to the helical transition surface. For the angle parameter of the helix, The angle parameter is the rotation around the axis of the cutter head. The pitch of the helical transition surface;

[0048] The geometric relationship corresponding to the helix angle of the helical transition surface is as follows:

[0049] ;

[0050] In the formula, The helix angle of the helical transition surface;

[0051] The helical transition surface is constrained based on the helical angle, specifically by setting constraint conditions. These constraints are as follows:

[0052] ;

[0053] In the formula, and These are the minimum and maximum helix angles, respectively.

[0054] This invention also provides a method for optimizing a milling cutter with a star-shaped cutting edge. This method is used to prepare the aforementioned milling cutter with a star-shaped cutting edge, comprising:

[0055] The initial value of the scale factor is determined based on the production target parameters, and the initial value of the scale factor is adjusted by the hardness value of the target material and the cutting process parameters to obtain the accurate scale factor of a single star-shaped cutting edge.

[0056] Construct a milling cutter model, determine the cutter head part of the milling cutter model, and establish a planar coordinate system with the center of the cutter head as the coordinate origin. Determine the parametric equations of a single star-shaped cutting edge, including precise scale factors and angle variation parameters.

[0057] The curvature of the star-shaped cutting edge is determined based on the parametric equation of a single star-shaped cutting edge. Multiple star-shaped cutting edges are then constructed, and each star-shaped cutting edge is rotated around the center of the cutting head at different angles to ultimately form multiple star-shaped cutting edges in different positions.

[0058] For the sharp corners of the star-shaped cutting edge, adjacent star-shaped cutting edges, and the connection between the star-shaped cutting edge and the cylindrical surface of the tool head, circular arcs, spline curves, and helical transition surfaces are used for transition connections, respectively. The transition connection methods are as follows:

[0059] Based on the cutting requirements, the radius of the transition arc is determined, and the tangent of the star-shaped line at the sharp corner is used as a reference to determine the center position of the transition arc. The equation of the transition arc is then determined, and the sharp corner of the star-shaped line cutting edge is transitioned by the arc.

[0060] On each star-shaped cutting edge, several key turning points are systematically selected. Based on the cubic spline interpolation algorithm, a continuous spline curve that passes through all the selected key points is constructed to achieve the transition connection between adjacent star-shaped cutting edges.

[0061] Based on the radius of the cutter head's cylindrical surface, and combined with the selected pitch and geometric parameters of the helical transition surface, the equation of the helical transition surface is constructed to determine the helical transition surface and realize the transition connection between the star-shaped cutting edge and the cutter head's cylindrical surface.

[0062] Compared with the prior art, the beneficial effects of the present invention are:

[0063] By precisely adjusting the scale factor of the milling cutter's cutting edge and combining it with cutting process parameters and material hardness, the cutting performance and durability of the milling cutter can be effectively improved. Scale factor optimization based on production target parameters can not only improve the cutting efficiency of the tool, but also reduce wear caused by changes in material properties and cutting conditions, thereby extending the tool's service life. This allows the milling cutter to maintain a stable cutting effect when facing target materials and processing environments, significantly improving the overall machining quality.

[0064] Furthermore, by employing various transition connection methods such as circular arcs, spline curves, and helical transition surfaces, the connection problem between the cutting edge of the tool and the cylindrical surface of the tool head is solved. The diverse transition connection methods not only improve the cutting performance of the tool, but also effectively reduce the stress concentration phenomenon that may occur during the cutting process, thereby improving the smoothness of the cutting process and the overall strength of the tool.

[0065] Secondly, by using a star-shaped cutting edge, the sudden curvature change during cutting will not cause a sharp change in force and impact, thereby reducing vibration, improving machining quality and efficiency, and reducing costs. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the overall structure of the milling cutter of the present invention;

[0067] Figure 2 A schematic diagram illustrating the coordinate system of the milling cutter head for this invention;

[0068] Figure 3 This is a schematic diagram of the overall method flow of the present invention;

[0069] Attached diagram: 1. Handle; 2. Blade body; 3. Blade tip. Detailed Implementation

[0070] 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.

[0071] 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.

[0072] Example:

[0073] Please see Figures 1-2 The present invention provides a technical solution:

[0074] A milling cutter with a star-shaped cutting edge, specifically comprising:

[0075] The milling cutter includes a shank 1, a cutter body 2, and a cutter head 3. The cutter body 2 connects the shank 1 and the cutter head 3. The cutter head 3 has at least three cutting edges designed based on a star-shaped profile distributed around its circumference. A milling cutter model is constructed based on the cutter's structure. The cutter head 3 portion of the milling cutter model is determined, and a planar coordinate system is established with the center of the cutter head 3 as the origin. The parameter equations for a single star-shaped cutting edge, including precise scale factors and angle variation parameters, are determined. The method for determining the cutting edges of the milling cutter is as follows:

[0076] The initial value of the scale factor is determined based on the production target parameters, and the initial value of the scale factor is adjusted by the hardness value of the target material and the cutting process parameters to obtain the accurate scale factor of a single star-shaped cutting edge.

[0077] The milling cutter specifically consists of a shank 1, a cutter body 2, and a cutter head 3. The cutter body 2 connects the shank 1 and the cutter head 3. The shank 1 connects to the milling machine spindle to transmit power. The cutter body 2 is made of high-strength alloy steel, which has high yield strength and can withstand large torque and bending moment, playing a supporting and torque-transmitting role. The cutter head 3 has no less than three cutting edges based on a star-shaped design distributed on its circumference. The cutter head 3 is the key part of cutting and is made of high-performance cemented carbide material YG8C, which has high hardness, high wear resistance, and good impact toughness. The cutting edges are symmetrically distributed to reduce vibration and improve cutting stability.

[0078] The initial value of the scale factor is determined based on the production target parameters, including the diameter of the cutting head 3 and the number of cutting edges. The specific formula used to calculate the initial value of the scale factor is as follows:

[0079] ;

[0080] In the formula, This is the initial value of the scaling factor. The cutter head has a diameter of 3. Number of cutting edges and This is an empirical coefficient, specifically set as follows: , ;

[0081] It should be noted that the diameter of the cutting head (3) is one of the important parameters affecting the cutting performance of the milling cutter. A larger diameter generally results in a larger cutting area and increased cutting capability. Therefore, it is treated as a numerator in the formula, directly affecting the value of the scale factor. The number of cutting edges directly relates to cutting efficiency and tool life. Multiple cutting edges can distribute the cutting load and improve cutting capability, but more cutting edges also mean that, for a given cutting head diameter (3), the cutting capability of a single cutting edge may decrease. Therefore, the formula uses (…) to… The number of cutting edges is used as the denominator to reflect the influence of the initial value of the scale factor.

[0082] The logic behind adjusting the initial value of the scale factor by processing the target material hardness value and cutting process parameters is as follows: The cutting process parameters include target values ​​for cutting speed and cutting feed rate. Based on the cutting process parameters and the target material hardness value, an adaptive adjustment factor is generated. The formula for calculating the adaptive adjustment factor is as follows:

[0083] ;

[0084] In the formula, As an adaptive adjustment factor, To determine the hardness value of the target material, This is a reference value for the hardness of the processed material. Set a target value for the cutting speed. This is a reference value for cutting speed. Set a target value for the cutting feed rate. This is a reference value for the cutting feed rate. , and Here are the weighting coefficients, where and , and All are greater than 0;

[0085] It should be noted that material hardness directly affects the ease of machining. Higher hardness means increased cutting force and wear on the tool during machining. This can be achieved by comparing the hardness values ​​of the target materials. Reference value for the hardness of the processed material The difference can quantify the impact of hardness changes on tool performance, thereby affecting the adaptive adjustment factor and subsequently adjusting the scale factor of the star-shaped line.

[0086] Cutting speed is a crucial parameter affecting machining efficiency and tool wear. Excessively high or low cutting speeds can negatively impact cutting quality and tool life. Setting target values ​​by comparing different cutting speeds is essential. and cutting speed reference value This allows for the assessment of the impact of speed variations on the machining process, thereby enabling the adjustment of the tool's dimensional factor.

[0087] The cutting feed rate also affects cutting efficiency and tool load. A higher feed rate may lead to tool overload, while a lower feed rate may lead to low machining efficiency. Therefore, we quantify its impact on tool performance, adjust the adaptive adjustment factor based on its impact on tool performance, and then adjust the scale factor of the star curve.

[0088] Among them, the reference value of the hardness of the target material being processed Cutting speed reference value and cutting feed rate reference value The general setting is: , , Among them, the hardness value of the target material being processed Specifically, this refers to the hardness value of the material being machined using the milling cutter of this invention in actual machining applications; and the target value for the cutting speed setting. The specific values ​​refer to the cutting speed values ​​and feed rate target values ​​specifically set by the milling cutter of this invention in actual machining applications. Specifically, this refers to the cutting feed rate set by the milling cutter of this invention in actual machining.

[0089] Hardness is a key factor affecting tool wear and cutting forces during the cutting process. Generally, the higher the hardness, the more difficult the cutting process and the higher the requirements for the tool. Therefore, material hardness has the most significant impact on tool performance. The weight of cutting speed is the highest, reflecting its importance in the cutting process. Cutting speed directly affects the cutting efficiency of the tool and the heat generated. An appropriate cutting speed can improve machining efficiency, but excessive speed will lead to accelerated tool wear. Therefore, the influence of cutting speed is second only to material hardness. The weight is second, therefore set and , and All are greater than 0; generally, for materials with low hardness, , and The setting range is 0.8-1.0; for materials with higher hardness, the setting range is 1.0-1.2.

[0090] The precise scaling factor is specifically calculated using an adaptive adjustment factor and an initial value for the scaling factor. The specific formula used for this calculation is as follows:

[0091] ;

[0092] In the formula, The precise scaling factor is used as the scaling factor for the single star-shaped cutting edge parameter equation.

[0093] Establish an XOY plane coordinate system with the center of cutter head 3 as the origin, flush with the cross-section of cutter head 3. For details on establishing the plane coordinate system with the center of cutter head 3 as the origin, please refer to [link to relevant documentation]. Figure 2 In the figure, o is the origin of the coordinate system, and the specific parametric equation of the single star-shaped cutting edge is as follows:

[0094] ;

[0095] In the formula, and These are the x-coordinate and y-coordinate of a planar coordinate system, respectively. Here are the parameters for the angular variation of the star-shaped line, where .

[0096] It should be noted that the star-shaped cutting edge parameter equation is established based on the standard star-shaped cutting edge parameter equation.

[0097] The curvature of the star-shaped cutting edge is determined based on the parameter equation of a single star-shaped cutting edge. Multiple star-shaped cutting edges are then constructed, and these multiple star-shaped cutting edges are rotated around the center of the cutter head 3 at different angles to ultimately form multiple star-shaped cutting edges in different positions.

[0098] The specific formula used to determine the curvature of the asteroid based on the precise scale factor is as follows:

[0099] ;

[0100] In the formula, The curvature of the asteroid is... Let be the first derivative of the x-coordinate of the star curve with respect to the angle variation parameter. Let be the first derivative of the ordinate of the star-shaped line with respect to the angle variation parameter. Let be the second derivative of the x-coordinate of the star curve with respect to the angle variation parameter. The second derivative of the ordinate of the star-shaped line with respect to the angle variation parameter;

[0101] Differentiating the parametric equations of a single star-shaped cutting edge and substituting them into the curvature formula of the star-shaped line, we obtain the simplified curvature formula for the star-shaped line, as follows:

[0102] ;

[0103] Where the maximum value of curvature k is taken as The minimum value is 0;

[0104] It should be noted that when =±1, that is When n=0, 1, 2, 3, the curvature Get the maximum value ;when =0, that is When n=0,1,2,3,4, the curvature To achieve the minimum value of 0, in practical applications, it can be achieved by adjusting... The value is used to change the curvature of the star-shaped line, thereby adapting to different processing requirements.

[0105] Rotate the multiple star-shaped cutting edges around the center of the cutter head 3 at different angles. The equation of the resulting curve is:

[0106] ;

[0107] In the formula, Let x be the x-coordinate of the k-th star-shaped cutting edge after rotation. Let y be the ordinate of the k-th star-shaped cutting edge after rotation. Let be the rotation angle of the k-th star-shaped cutting edge, where k is the index of the star-shaped cutting edge.

[0108] The rotation angle of the k-th star-shaped cutting edge The specific formula used for the calculation is as follows:

[0109] ;

[0110] In the formula, This represents the total number of star-shaped cutting edges.

[0111] To ensure more uniform cutting with the milling cutter, the multiple star-shaped cutting edges in the initial state are rotated around the center of the cutter head 3 at different angles. This ultimately results in multiple star-shaped cutting edges at different locations.

[0112] For the sharp corners of the star-shaped cutting edge, adjacent star-shaped cutting edges, and the connection between the star-shaped cutting edge and the cylindrical surface of the tool head, circular arcs, spline curves, and spiral transition surfaces are used for transition connections, respectively. The transition connection methods are as follows:

[0113] Based on the cutting requirements, the radius of the transition arc is determined, and the tangent of the star-shaped line at the sharp corner is used as a reference to determine the center position of the transition arc. The equation of the transition arc is then determined, and the sharp corner of the star-shaped line cutting edge is transitioned by the arc.

[0114] On each star-shaped cutting edge, several key turning points are systematically selected. Based on the cubic spline interpolation algorithm, a continuous spline curve that passes through all the selected key points is constructed to achieve the transition connection between adjacent star-shaped cutting edges.

[0115] Based on the radius of the cylindrical surface of the cutter head 3, and combined with the selected pitch and geometric parameters of the helical transition surface, the equation of the helical transition surface is constructed to determine the helical transition surface and realize the transition connection between the star-shaped cutting edge and the cylindrical surface of the cutter head 3.

[0116] For the sharp corners of the star-shaped cutting edge, a rounded transition is used. The logic for determining the specific radius of the transition arc is as follows: The cutting requirements include: the hardness value of the target material, the target value of the cutting force, the target value of the cutting speed, and the target value of the cutting depth. Based on the cutting requirements and combined with the diameter parameter of the tool head 3, the formula for determining the specific radius of the transition arc is as follows:

[0117] ;

[0118] In the formula, The radius of the transition arc. Set a target value for the machining cutting force. Set a target value for the depth of cut. To achieve the maximum cutting force during machining, This represents the maximum cutting speed. This represents the maximum depth of cut. This represents the maximum diameter of the cutter head (3). , , and The weighting coefficient is specifically set as follows: , , , and It is a non-linear exponent. ;

[0119] Setting target value for machining cutting force Specifically, this refers to the machining cutting force set by the milling cutter of this invention in actual machining; and the target value for the cutting depth set. Specifically, it refers to the cutting depth value required by the milling cutter of this invention in actual machining;

[0120] The maximum values ​​of machining cutting force, cutting speed, cutting depth, and tool head diameter are set based on the maximum values ​​used in historical machining data.

[0121] It should be noted that the star-shaped cutting edge has sharp corners, which can easily lead to stress concentration during cutting, resulting in tool wear or even chipping. Therefore, a rounded transition is used at the sharp corners of each star-shaped cutting edge. The selection of the transition radius r is crucial, as it is closely related to the tool's durability and cutting performance.

[0122] Hardness value of the target material being processed The hardness of a material indicates its resistance to deformation. Higher material hardness increases machining difficulty, and also increases the load and wear on the cutting tool during cutting. Sharp corners are also more prone to chipping. Therefore, the hardness value of the target material is crucial for machining. The increase requires a larger transition radius r to reduce stress concentration at sharp corners and improve tool life.

[0123] Cutting force is the main load source generated during the cutting process of a tool, and it directly affects the stress distribution of the tool. The greater the cutting force, the more obvious the stress concentration at the tool tip. Therefore, the greater the cutting force, the larger the transition radius r needs to be to disperse the stress and reduce the risk of chipping at the sharp corner.

[0124] Cutting speed affects the friction and heat generation between the tool and the workpiece. Higher cutting speeds lead to increased temperatures in the tool tip area, which reduces the strength and wear resistance of the tool material, increasing the risk of chipping or wear. Therefore, higher cutting speeds require larger transition radius.

[0125] The depth of cut affects the cutting load on the tool. A larger depth of cut will subject the tool to greater cutting forces, especially in sharp corner areas where chipping is more likely. Therefore, as the depth of cut increases, the radius of curvature needs to be increased.

[0126] Larger tool diameters typically have higher structural strength and less impact on stress distribution at sharp corners; therefore, increasing the tool diameter reduces the need for arc radius.

[0127] The logic for determining the center position of the transition arc is as follows: taking the tangent of the star-shaped line at the sharp corner as the reference, the center of the transition arc is located perpendicular to the tangent and at a distance from the vertex of the sharp corner equal to the radius of the transition arc. The arc equation is determined by this center and radius, thereby transitioning the sharp corner of the star-shaped line, achieving a smooth transition of the sharp corner, and reducing stress concentration.

[0128] The logic behind determining the spline curve for the transition connection between adjacent star-shaped cutting edges is as follows: Several key turning points are systematically selected, including the starting point, ending point, and several turning points in the region between them. Based on these key turning points, a spline curve is determined using a spline interpolation algorithm. The calculation formula for spline interpolation is:

[0129] ;

[0130] In the formula, For spline curve functions, Let the position of the spline curve be the independent variable. , , and For the coefficients to be determined, interpolation calculations are performed using the cubic spline interpolation formula. The specific logic for determining the coefficients is as follows: a system of linear equations is established based on the constraints of the function values ​​and derivative values ​​of the spline curve to solve for the coefficients of the spline curve. Specifically, the continuity of the spline curve function values, first derivative, and second derivative is used as periodic boundary conditions to determine the coefficients to be determined; the periodic boundary conditions are specifically set as follows:

[0131] ;

[0132] In the formula, and These are the start and end points of the spline curve, respectively. and These are the first derivatives at the start and end points of the spline curve, respectively. and These are the second derivatives at the start and end points of the spline curve, respectively.

[0133] Three to five points are evenly selected in the middle region between the starting and ending points of each star-shaped cutting edge to determine the key turning points. This ensures that the spline curve accurately reflects the geometry of the cutting edge and the distribution of cutting forces. Interpolation calculations are performed using the cubic spline interpolation formula, ensuring the continuity of the first and second derivatives to achieve a smooth transition. This ensures that the cutting edge can smoothly transition from one cutting edge to another during the milling process, reducing abrupt changes in cutting forces and improving the surface finish.

[0134] The selected corresponding points are used as nodes for spline interpolation. Periodic boundary conditions are chosen to ensure the overall smoothness and continuity of the spline curve. A system of linear equations is established based on the constraints of the function values ​​and derivative values ​​of the spline curve to solve for the coefficients of the spline curve. The continuity of the first derivative at the connection points is ensured to guarantee the smoothness of the curve. The continuity of the second derivative is ensured to further guarantee the smoothness of the curve and reduce the sudden changes in cutting force.

[0135] The geometric parameters of the helical transition surface specifically include: the radius of the cylindrical surface of the cutter head 3, the distance from the center of the cutter head 3 to the helical transition surface, the angle parameter of the helix, and the angle parameter of rotation around the axis of the cutter head 3. The specific equation of the helical transition surface is as follows:

[0136] ;

[0137] In the formula, , and These represent the abscissa, ordinate, and perpendicular coordinates of the spiral transition surface, respectively. The radius of the cylindrical surface of the cutter head is 3. This is the distance from the center of the cutter head 3 to the helical transition surface. For the angle parameter of the helix, The angle parameter is the rotation around the three axes of the cutter head. The pitch of the helical transition surface;

[0138] The geometric relationship corresponding to the helix angle of the helical transition surface is as follows:

[0139] ;

[0140] In the formula, The helix angle of the helical transition surface;

[0141] The helical transition surface is constrained based on the helical angle, specifically by setting constraint conditions. These constraints are as follows:

[0142] ;

[0143] In the formula, and These are the minimum and maximum helix angles, respectively.

[0144] The transition between the star-shaped cutting edge and the cylindrical surface of the tool tip (3) is a crucial step in optimizing cutting force transmission and improving the overall cutting performance of the tool. A helical transition surface connects the star-shaped cutting edge and the cylindrical surface of the tool tip (3), achieving a smooth connection, reducing stress concentration, optimizing cutting force transmission, and improving the overall cutting performance of the tool. This smooth connection effectively avoids abrupt changes in cutting force and impacts caused by sudden curvature variations.

[0145] helix angle of helical transition surface and pitch This is an important parameter. Helix angle The value range is generally within to Between different helix angles, a smaller helix angle provides a smoother transition but may increase the transition length; a larger helix angle can shorten the transition length but may cause stress concentration; choosing the appropriate helix angle requires comprehensive consideration of the tool stiffness and the distribution of cutting forces. Pitch The pitch is determined based on the size of the cutter head and machining requirements. A smaller pitch can provide a finer transition, but may increase manufacturing difficulty; a larger pitch can simplify the manufacturing process, but may affect the smoothness of the transition. The typical range is 0.5-2mm.

[0146] The angle parameter of the helix Angular parameters of rotation around the three axes of the cutter head .

[0147] Based on the above design, the rake angle and clearance angle of the cutting tool are determined: according to the properties of the workpiece and the cutting conditions, the rake angle is selected as follows: The value of the back angle should be adjusted according to the properties of the material being processed and the cutting conditions; the range of the back angle is... A reasonable clearance angle can reduce friction and wear between the tool's flank face and the machined surface of the workpiece, thus extending the tool's service life.

[0148] Please see Figure 3 The present invention also provides a method for optimizing a milling cutter with a star-shaped cutting edge. This method is used to prepare the aforementioned milling cutter with a star-shaped cutting edge, comprising:

[0149] Step 1: Determine the initial value of the scale factor based on the production target parameters, and adjust the initial value of the scale factor by processing the target material hardness value and cutting process parameters to obtain the accurate scale factor of a single star-shaped cutting edge;

[0150] Step 2: Construct the milling cutter model, determine the cutter head 3 part of the milling cutter model, and establish a plane coordinate system with the center of the cutter head 3 as the coordinate origin. Determine the single star-shaped cutting edge parameter equation containing the precise scale factor and angle change parameters.

[0151] Step 3: Determine the curvature of the star-shaped line based on the parameter equation of a single star-shaped cutting edge, thereby constructing multiple star-shaped cutting edges. Rotate the multiple star-shaped cutting edges around the center of the cutter head 3 at different angles to finally form multiple star-shaped cutting edges in different positions.

[0152] Step 4: For the sharp corners of the star-shaped cutting edge, adjacent star-shaped cutting edges, and the connection between the star-shaped cutting edge and the cylindrical surface of the tool head 3, use circular arcs, spline curves, and spiral transition surfaces for transition connections, respectively. The transition connection methods are as follows:

[0153] Based on the cutting requirements, the radius of the transition arc is determined, and the tangent of the star-shaped line at the sharp corner is used as a reference to determine the center position of the transition arc. The equation of the transition arc is then determined, and the sharp corner of the star-shaped line cutting edge is transitioned by the arc.

[0154] On each star-shaped cutting edge, several key turning points are systematically selected. Based on the cubic spline interpolation algorithm, a continuous spline curve that passes through all the selected key points is constructed to achieve the transition connection between adjacent star-shaped cutting edges.

[0155] Based on the radius of the cylindrical surface of the cutter head 3, and combined with the selected pitch and geometric parameters of the helical transition surface, the equation of the helical transition surface is constructed to determine the helical transition surface and realize the transition connection between the star-shaped cutting edge and the cylindrical surface of the cutter head 3.

[0156] 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.

[0157] 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.

[0158] 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.

[0159] 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 milling cutter having a star wire edge, characterized by: The milling cutter comprises a shank, a cutter body and a cutter head, the cutter body is used for connecting the shank and the cutter head, the cutter head is circumferentially distributed with not less than three blade edges based on star-shaped line design, a milling cutter model is constructed according to the structure of the milling cutter, the cutter head part of the milling cutter model is determined, a plane coordinate system is established with the center of the cutter head as the coordinate origin, a single star-shaped line blade edge parameter equation containing an accurate scale factor and an angle change parameter is determined, and the blade edge determination method of the milling cutter is as follows: An initial value of the scale factor is determined based on a production target parameter, and the initial value of the scale factor is adjusted through a machining target material hardness value and a cutting process parameter to obtain the accurate scale factor of the single star-shaped line blade edge; The curvature of the star-shaped line is determined according to the single star-shaped line blade edge parameter equation, a plurality of star-shaped line blade edges are constructed, and the plurality of star-shaped line blade edges are respectively rotated by different angles around the center of the cutter head to finally form a plurality of star-shaped line blade edges at different positions; For the sharp corners of the star-shaped line blade edge, adjacent star-shaped line blade edges and the star-shaped line blade edge and the cylindrical surface of the cutter head, a circular arc, a spline curve and a spiral transition surface are respectively used for transition connection, and the transition connection method is as follows: A transition circular arc radius is determined through a cutting machining requirement, a transition circular arc center position is determined with the tangent of the star-shaped line at the sharp corner as a reference, the transition circular arc equation is determined, and the sharp corner of the star-shaped line blade edge is circularly arc transitioned; On each star-shaped line blade edge, a plurality of turning key points are selected, a continuous spline curve passing through all the selected key points in sequence is constructed based on a cubic spline interpolation algorithm, and the transition connection of adjacent star-shaped line blade edges is realized; Based on the radius of the cylindrical surface of the cutter head, the spiral transition surface equation is constructed in combination with the selected pitch and the geometric parameters of the spiral transition surface, the spiral transition surface is determined, and the transition connection of the star-shaped line blade edge and the cylindrical surface of the cutter head is realized.

2. The milling cutter with star-shaped line blade edges according to claim 1, characterized in that: An initial value of the scale factor is determined based on a production target parameter, the production target parameter comprises a cutter head diameter and a blade edge number, and the formula on which the calculation of the initial value of the scale factor is specifically based is: ； In the formula, is the initial value of the scale factor, is the diameter of the tool head, is the number of cutting edges, and is an empirical coefficient, which is set to , ; The initial value of the scale factor is adjusted through a machining target material hardness value and a cutting process parameter, and the logic on which the adjustment is specifically based is that the cutting process parameter comprises a cutting speed setting target value and a cutting feed amount setting target value, an adaptive adjustment factor is generated based on the cutting process parameter in combination with the machining target material hardness value, and the formula on which the calculation of the adaptive adjustment factor is specifically based is: ； wherein is an adaptive adjustment factor, is a hardness value of the target material to be processed, is a reference value of the hardness of the material to be processed, is a target value of the cutting speed, is a reference value of the cutting speed, is a target value of the cutting feed amount, is a reference value of the cutting feed amount, , and are weight coefficients, wherein and , and are all greater than 0. The accurate scale factor is calculated by the adaptive adjustment factor and the initial value of the scale factor, and the formula on which the calculation is specifically based is: ； In the formula, As a precise scale factor, the precise scale factor is taken as a scale factor of a single star-shaped line blade edge parameter equation.

3. The milling cutter with star-shaped line blade edges according to claim 2, characterized in that: An XOY plane coordinate system flush with the cutter head transverse plane is established with the center of the cutter head as the coordinate origin, and the single star-shaped line blade edge parameter equation is specifically as follows: ； wherein and are the horizontal and vertical coordinates of the planar coordinate system, respectively, is the angle variation parameter of the star line, wherein .

4. The milling cutter having a star-shaped wire edge according to claim 3, characterized in that: The formula on which the determination of the curvature of the star-shaped line based on the accurate scale factor is specifically based is: ； wherein is the first derivative of the star line ordinate with respect to the angle variation parameter, is the first derivative of the star line abscissa with respect to the angle variation parameter, is the first derivative of the star line ordinate with respect to the angle variation parameter, is the second derivative of the star line abscissa with respect to the angle variation parameter, is the second derivative of the star line ordinate with respect to the angle variation parameter. The derivative of the single star-shaped line blade edge parameter equation is taken and substituted into the curvature formula of the star-shaped line to obtain a simplified formula of the curvature of the star-shaped line, which is specifically as follows: ； where the maximum value of the curvature k is taken at and the minimum value is taken at 0; The plurality of star-shaped line blade edges are respectively rotated by different angles around the center of the cutter head, and the curve equation after rotation is as follows: ； In the formula, is the horizontal coordinate of the kth star-shaped line after rotation, is the vertical coordinate of the kth star-shaped line after rotation, is the rotation angle of the kth star-shaped line, and k is the index of the star-shaped line.

5. The milling cutter having a star-shaped wire edge according to claim 4, characterized in that: The logic for determining the specific radius of the transition arc for the sharp corner of the star-shaped line edge is as follows: the cutting processing requirements include: the target material hardness value, the cutting force setting target value, the cutting speed setting target value, and the cutting depth setting target value; based on the cutting processing requirements, the transition arc radius is determined in combination with the tool head diameter parameter; the formula for determining the specific transition arc radius is: ； In the formula, is a transition arc radius, is a target value of a machining cutting force, is a target value of a cutting depth, is a maximum value of a machining cutting force, is a maximum value of a cutting speed, is a maximum value of a cutting depth, is a maximum value of a tool head diameter, , , and are weight coefficients, and are specifically set as , , , and are nonlinear indexes, ; The logic for determining the specific position of the transition arc center is as follows: taking the tangent of the star-shaped line at the sharp corner as the reference, the center of the transition arc is located perpendicular to the tangent, and the distance from the sharp corner vertex is the transition arc radius; the arc equation is determined through the center and the radius to transition the sharp corner of the star-shaped line edge.

6. The milling cutter having a star wire edge according to claim 1, characterized in that: The logic for determining the spline curve for the transition connection between adjacent star-shaped line edges is as follows: a number of turning key points are systematically selected, including the starting point, the end point, and a number of turning points in the region between them; the spline curve is determined based on the turning key points through the spline interpolation algorithm; the calculation formula for spline interpolation is: ； In the formula, is a spline curve function, is a position independent variable of the spline curve, , , and are undetermined coefficients, and the undetermined coefficients are determined by using a cubic spline interpolation formula for interpolation calculation. The logic for determining the undetermined coefficients is that a linear equation group is established based on the constraint conditions of the function value and the derivative value of the spline curve to solve the coefficients of the spline curve. Specifically, the undetermined coefficients are determined by taking the function value, the first-order derivative, and the second-order derivative of the spline curve as periodic boundary conditions. The periodic boundary conditions are specifically set as: ； wherein and are the first derivative at the start and end of the spline curve, respectively, and are the first derivative at the start and end of the spline curve, respectively, and are the second derivative at the start and end of the spline curve, respectively.

7. The milling cutter having a star wire edge according to claim 1, characterized in that: The geometric parameters of the spiral transition surface include: the tool head cylindrical surface radius, the distance from the tool head center to the spiral transition surface, the angle parameter of the spiral line, and the angle parameter of rotation around the tool head axis; the specific spiral transition surface equation is: ； wherein , and are the transverse, longitudinal and vertical coordinates of the helical transition surface, respectively, is the radius of the tool cylinder surface, is the distance from the tool center to the helical transition surface, is the angular parameter of the helix, is the angular parameter of the rotation around the tool axis, is the pitch of the helical transition surface; The geometric relationship corresponding to the spiral angle of the spiral transition surface is: ； In the formula, is the helix angle of the helical transition surface; The spiral transition surface is constrained based on the spiral angle, and the constraint is specifically implemented by setting a constraint condition, which is: ； wherein and are the minimum helix angle and the maximum helix angle, respectively.

8. A method of optimizing a milling cutter having a star wire edge, characterized by: The optimization method of the milling cutter with a star-shaped line edge is used to prepare the milling cutter with a star-shaped line edge according to any one of claims 1-7, comprising: Based on the production target parameters, the initial value of the scale factor is determined, and the initial value of the scale factor is adjusted through the target material hardness value and the cutting process parameters to obtain the accurate scale factor of the single star-shaped line edge; A milling cutter model is constructed, the tool head part of the milling cutter model is determined, and a plane coordinate system is established with the tool head center as the coordinate origin to determine the single star-shaped line edge parameter equation containing the accurate scale factor and the angle change parameter; According to the single star-shaped line edge parameter equation, the curvature of the star-shaped line is determined, and a plurality of star-shaped line edges are constructed, and the plurality of star-shaped line edges are rotated by different angles around the tool head center to finally form a plurality of star-shaped line edges at different positions; The sharp corner of the star-shaped line edge, the adjacent star-shaped line edge, and the star-shaped line edge and the tool head cylindrical surface are respectively transitionally connected by a circular arc, a spline curve, and a spiral transition surface, and the transition connection method is as follows: The transition arc radius is determined based on the cutting processing requirements, and the transition arc center position is determined based on the tangent of the star-shaped line at the sharp corner, and the transition arc equation is determined to perform arc transition on the sharp corner of the star-shaped line edge. On each star-shaped line edge, a number of turning key points are systematically selected, and a continuous spline curve passing through all selected key points is constructed based on the cubic spline interpolation algorithm to realize the transition connection between adjacent star-shaped line edges. Based on the tool head cylindrical surface radius, the selected pitch, and the geometric parameters of the spiral transition surface, the spiral transition surface equation is constructed to determine the spiral transition surface and realize the transition connection between the star-shaped line edge and the tool head cylindrical surface.

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