A milling cutter for machining complex curved surfaces

Abstract

This invention provides a milling cutter for machining complex curved surfaces, relating to the field of milling cutter design technology. Specific steps include: constructing a three-dimensional Cartesian coordinate system; constructing an oval-shaped turning surface based on the three-dimensional Cartesian coordinate system; and uniformly arranging... Each cutting edge is used to generate a cutting edge profile along a right-handed helical trajectory. Combined with preset tool angle parameters, a solid model of the milling cutter and the complex curved surface to be machined are formed. The tool contact point trajectory and sampling point coordinates are obtained using a cross-sectional plane. Utilizing the tangential relationship between the oval-shaped rotary surface and the curved surface at the tool contact point, the tool position trajectory is derived and solved. This completes the overall design of the oval-shaped rotary surface and the milling cutter. The variable curvature rotary surface of this invention can better match the concave and convex shapes of complex curved surfaces, enabling precise contact between the oval-shaped rotary surface and each tool contact point on the curved surface. Compared to the point-contact machining method in existing technologies, this effectively avoids over-cutting and under-cutting problems, improving the machining accuracy and surface quality of complex curved surfaces.

Description

A milling cutter for machining complex curved surfaces Technical Field

[0001] This invention relates to the field of milling cutter design technology, specifically to a milling cutter for machining complex curved surfaces. Background Technology

[0002] In traditional milling, ball end mills have limitations when machining complex curved surfaces due to their simple cutting edge geometry and limited adaptability. For example, although ball end mills can achieve multi-directional cutting, their contact area is small, their cutting efficiency is low, and residual material tends to accumulate in the transition area of ​​the curved surface, leading to cumbersome subsequent finishing processes.

[0003] In existing technologies, the solution of tool position trajectory in machining complex curved surfaces relies on empirical algorithms that "fixedly offset the tool contact point along the normal of the surface." That is, based on the tool radius, the extracted tool contact point is offset by a fixed distance along the normal of the surface to be machined to directly obtain the tool position coordinates. This method ignores the geometric fit between the tool head's rotating surface and the surface to be machined, which has significant drawbacks. For milling cutters with variable curvature heads, such as oval heads, fixed normal offset cannot guarantee that the tool head's rotating surface and the surface are tangent at the tool contact point. It can only achieve "rough alignment" rather than "precise fit," resulting in a serious lack of fit between the tool and the surface. This leads to excessive residual height and large accuracy deviation in subsequent machining of the surface.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a milling cutter for machining complex curved surfaces, 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:

[0007] A milling cutter for machining complex curved surfaces, the milling cutter comprising a head and a shank, one end of the shank being coaxially and fixedly connected to the head, and the other end of the shank being away from the shank and integrally formed with an oval-shaped rotating surface on the outer circumferential surface of the head, wherein the design method of the oval-shaped rotating surface includes the following steps:

[0008] S1. Construct a three-dimensional rectangular coordinate system, and based on the three-dimensional rectangular coordinate system, construct the basic surface model of the oval-shaped revolution surface;

[0009] S2. Based on the basic surface model of the oval head revolution surface, obtain the surface profile of the oval head revolution surface, and evenly distribute it along the circumferential direction of the milling cutter. Each cutting edge generates a cutting edge profile along a right-hand spiral trajectory at its installation position, and the first rake face and the first flank face are machined according to preset tool angle parameters to form a milling cutter solid model, while simultaneously constructing the complex curved surface to be machined.

[0010] S3. Adopting parallel to The plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory. The three-dimensional coordinates of each sampling point are extracted. Using the geometric relationship that the egg-shaped rotating surface and the complex curved surface to be processed are tangent at the tool contact point, the tool position trajectory equation is derived and the motion trajectory of the tool position point is obtained by solving it.

[0011] S4. Simulate the cutting process of the oval-shaped rotating surface on the complex curved surface based on the motion trajectory of the tool position, and complete the overall design of the oval-shaped rotating surface and the milling cutter.

[0012] Furthermore, the three-dimensional Cartesian coordinate system has the tool center point as the origin. With the direction of the milling cutter axis as The axis is defined as the direction outward from the radial section of the tool holder passing through the origin along the tool radius. Axis, determined by the right-hand rule Three-dimensional rectangular coordinate system of axes .

[0013] Furthermore, the blade head includes an end cutting edge and a peripheral cutting edge, and the generatrix of rotation of the end cutting edge adopts an oval curve, which is constructed on... In a rectangular coordinate system Within the second and third quadrants of the plane;

[0014] The two points that are furthest from the egg-shaped curve to its axis of symmetry are taken as the endpoints of the egg-shaped curve's symmetry, denoted as . and endpoint and The connecting line is a transition arc. ;

[0015] The oval curve of the end cutting edge is tangent to the transition arc of the circumferential cutting edge at the end point. Furthermore, the oval curve and the transition arc The connection uses equal curvature, i.e., tangential;

[0016] endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is ;

[0017] The equation for the egg-shaped curve is expressed as:

[0018]

[0019] in, Indicates the egg-shaped curve at The coordinate components of the axis, Indicates the egg-shaped curve at The coordinate components of the axis, The major radius of the oval curve, The short radius of the oval curve, This is the morphological adjustment coefficient for the egg-shaped curve. , Let be the parameter angle of the egg-shaped curve. ;

[0020] radius of transition arc With tool radius satisfy:

[0021] Transition arc The coordinates of the center of the circle are The equation for the transition circle arc is expressed as:

[0022]

[0023] in, Indicates the transition arc at The coordinate components of the axis, Indicates the transition arc at The coordinate components of the axis, The parameter angle is the transition arc.

[0024] Furthermore, the oval-shaped rotating surface is composed of an oval curve and a transition arc. Axis rotation generation:

[0025] Egg-shaped curve Rotating the shaft 360° yields the end-cutting edge rotation surface, the equation of which is:

[0026]

[0027] in, They represent any point on the egg-shaped surface at... axis, axis, The coordinate components of the axis, For the egg-shaped curve The angle of rotation of the axis;

[0028] The end-cutting surface is a variable curvature rotary surface, corresponding to the tip cutting area of ​​the tool head;

[0029] Rotate the transition arc around Rotating the axis by 360° yields the transition zone surface, whose equation is expressed as:

[0030]

[0031] in, They represent any point on the transition arc surface at... axis, axis, The coordinate components of the axis, For transition arc The angle of rotation of the axis;

[0032] The connecting area surface is a fixed curvature rotation surface, corresponding to the connecting transition area between the cutting area at the tip of the tool head and the side of the tool holder;

[0033] The cutting edge area and the transition area are smoothly joined along their common boundary to form a complete oval-shaped rotating surface.

[0034] Furthermore, the end cutting edge is provided with a front cutting edge and a rear cutting edge, and the peripheral cutting edge is provided with a front cutting edge and a rear cutting edge.

[0035] Furthermore, the complex surface to be processed is constructed, and the specific logic is as follows:

[0036] Using the oval-shaped rotating surface as a reference, and centering on the center of the oval-shaped rotating surface, evenly distributed along its circumference. Each blade, arranged in 360° / The included angle is used to define the blade mounting positions. The blade profile is generated along the right-hand helical trajectory of each blade mounting position. The parametric equation of the right-hand helical is:

[0037]

[0038] in, For any point on the spiral, axis, axis, Axis coordinate components, For spiral winding The rotation angle of the shaft, , For spiral winding The number of revolutions of the axis, The helix angle;

[0039] The preset tool angle parameters include the front angle, the first rear angle, and the second rear angle;

[0040] Simultaneously, chip grooves are reserved between adjacent cutting edges, and the first rake face is machined. With the first back face First rake face With the first back face The equation for the oval transition curve at the connection point is:

[0041]

[0042] in, For any point on the egg-shaped transition curve, axis, The coordinate components of the axis, The transition curves of the egg shape are respectively at In the coordinate system axis, Axis translation amount, The transition curve for the egg-shaped shape is around the origin. rotation angle, The parameter angle of the egg-shaped transition curve. , The initial parameter angle of the transition curve, It is a wedge angle;

[0043] The cutting edge contour conforms to the rake face, flank face, rake face, and flank face of the end cutting edge of the oval-shaped rotating surface. The rake face and flank face are machined according to the preset tool angle parameters to form a solid model of the milling cutter containing the cutting edge and chip groove, thereby constructing the complex curved surface to be machined.

[0044] Furthermore, adopting parallel to The cutting plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory. The three-dimensional coordinates of each point are extracted. The specific logic is as follows:

[0045] By parallel to The planar cutting plane is used to cut the complex curved surface to be processed into layers. Axis coordinates The equation of the cross-sectional plane corresponding to the layer height in CNC machining is: , For the first A cross-section Axis coordinates For the index of the cutting plane, , This represents the total number of cross-sectional planes.

[0046] Curvature analysis is performed on the complex surface to be processed. The equation of the complex surface to be processed is as follows:

[0047]

[0048] in, This is the equation expression for the complex surface to be processed. For any point on the complex surface to be processed, In coordinate system The coordinate components of the axis The coordinate components of the axis The coordinate components of the axis, These are the first shape control parameters and the second shape control parameters of the complex curved surface to be processed, respectively. This is the matrix transpose.

[0049] Calculate the curvature at any point on the complex surface to be processed. For surface regions where the rate of change of curvature is less than a threshold, the range of values ​​for the intersecting plane spacing is: For surface regions where the rate of curvature change is not less than the curvature change threshold, the range of values ​​for the intersecting plane spacing is: ;

[0050] The intersection of the cutting plane and the complex curved surface to be processed is the tool contact point trajectory. Multiple sampling points along the tool contact point trajectory are used to obtain the three-dimensional coordinates of the tool contact point. The three-dimensional coordinate vector of the tool contact point is represented as:

[0051]

[0052] in, The three-dimensional coordinate vector of the knife contact point. For the index of the sampling point, , The number of sampling points, The knife contact points are respectively Each sampling point is axis, axis, The coordinate components of the axis, For the first The first shape control parameter for each sampling point For the first The second shape control parameter for each sampling point.

[0053] Furthermore, by utilizing the geometric relationship that the oval-shaped rotating surface is tangent to the complex curved surface to be machined at the tool contact point, the equation of the tool position trajectory is derived and solved to obtain the motion trajectory of the tool position. The specific logic is as follows:

[0054] The tool position point, serving as the center of rotation of the milling cutter, is indirectly determined through the constraint that the milling cutter is tangent to the complex curved surface to be machined. Specifically, it is based on two conditions:

[0055] First, the common point condition: the tool contact point is both on the complex curved surface to be machined and on the milling cutter's rotating surface. The milling cutter's rotating surface only refers to the oval-shaped head rotating surface that participates in the cutting.

[0056] The implicit equation for the milling cutter's revolution surface is:

[0057]

[0058] in, For any point on the rotating surface of the milling cutter, axis, axis, The coordinate components of the axis, The knife point is located at axis, axis, The coordinate components of the axes;

[0059] Second, the condition of equal normal vectors is that the unit normal vectors of the milling cutter's rotating surface and the complex curved surface to be machined are completely consistent at the tool contact point.

[0060] The unit normal vector of the complex curved surface to be machined at the tool contact point for:

[0061]

[0062] in, The unit normal vectors are respectively in axis, axis, The coordinate components of the axes;

[0063] Taking the partial derivative of the function on the left-hand side of the implicit equation of the surface of revolution, we obtain the gradient vector. :

[0064] in, Implicit function pairs of the surface of revolution axis, axis, First-order partial derivatives of the axial coordinates;

[0065] in:

[0066]

[0067]

[0068]

[0069] The magnitude of the gradient vector for:

[0070]

[0071] Therefore, the unit normal vector of the milling cutter's rotating surface for:

[0072]

[0073] By solving the equations showing the equality of two normal vectors, and substituting the three-dimensional coordinates of the tool contact point, we obtain the three-dimensional coordinates of the corresponding tool position point. The three-dimensional coordinates of the tool position point are expressed as:

[0074]

[0075] in, The knife contact points are respectively at axis, axis, The coordinate components of the axis, Transition parameters;

[0076] Connect all tool points corresponding to the cutting planes according to the following rules:

[0077] Within the same cross-sectional plane, the first shape control parameter and the second shape control parameter of the complex curved surface to be processed are sorted in ascending order;

[0078] Between different cross-sectional planes, according to the cross-sectional plane Axis coordinates Increasing sort;

[0079] Ultimately, a spiral continuous trajectory is formed that covers the complex curved surface to be processed, which is the motion trajectory of the tool position point.

[0080] Compared with the prior art, the beneficial effects of the present invention are:

[0081] This invention constructs a three-dimensional rectangular coordinate system and builds a basic surface model of the oval-shaped end mill based on the three-dimensional rectangular coordinate system. This breaks through the crude mode of simplifying the tool into a "single-radius sphere" in the existing technology. Then, based on the oval-shaped end mill, the cutting edge contour is generated along the right-hand spiral trajectory of each cutting edge installation position. Combined with preset tool angle parameters, a solid model of the end mill is formed. This design enables the variable curvature surface of the oval-shaped end mill to better match the concave and convex shape of complex curved surfaces, avoiding the rough alignment problem caused by the "disconnect between the tool and the surface features" in the existing technology.

[0082] Define the curvature range and dimensions of the complex surface to be processed in order to construct the complex surface, using a method parallel to... The plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory. The three-dimensional coordinates of each sampling point are extracted. By utilizing the geometric relationship that the oval-shaped rotating surface and the complex curved surface to be processed are tangent at the tool contact point, the tool position trajectory equation is derived and the motion trajectory of the tool position point is obtained. This design enables the oval-shaped rotating surface to achieve precise contact with each tool contact point of the curved surface. Compared with the point contact processing method in the existing technology, it effectively avoids the problems of over-cutting and under-cutting, and improves the processing accuracy and surface quality of complex curved surfaces. Attached Figure Description

[0083] Figure 1 is a schematic diagram of the design method of the egg-shaped rotating surface of the present invention;

[0084] Figure 2 is a schematic diagram of the overall egg-shaped end mill of the present invention;

[0085] Figure 3 is a schematic diagram of the egg-shaped curve of the present invention;

[0086] Figure 4 is a schematic diagram of the end cutting edge of the egg-shaped end mill of the present invention;

[0087] In the diagram, 1 represents the head of the cutter, 2 represents the handle, 1-1 represents the end cutting edge, 1-2 represents the peripheral cutting edge, 3 represents the front face of the end cutting edge, 4 represents the front face of the peripheral cutting edge, 5 represents the back face of the end cutting edge, 6 represents the back face of the peripheral cutting edge, and 7 represents the chip groove. Detailed Implementation

[0088] 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.

[0089] 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.

[0090] Example:

[0091] Please refer to Figures 1-4. This invention provides a technical solution:

[0092] A milling cutter for machining complex curved surfaces, as shown in Figure 2, includes a cutter head 1 and a cutter shank 2. One end of the cutter shank 2 is coaxially and fixedly connected to the cutter head 1. An oval-shaped rotating surface is integrally formed on the outer circumferential surface of the cutter head 1 at the end away from the cutter shank 2. The design method of the oval-shaped rotating surface includes the following steps:

[0093] S1. Construct a three-dimensional rectangular coordinate system, and based on the three-dimensional rectangular coordinate system, construct the basic surface model of the oval-shaped revolution surface;

[0094] Based on the above embodiments, the three-dimensional rectangular coordinate system has the tool center point as the origin. With the direction of the milling cutter axis as The axis is defined as the direction outward from the radial section of the tool holder passing through the origin along the tool radius. Axis, determined by the right-hand rule Three-dimensional rectangular coordinate system of axes .

[0095] Based on the above embodiment, as shown in Figure 2, the blade head 1 includes an end cutting edge 1-1 and a peripheral cutting edge 1-2. The rotation generatrix of the end cutting edge 1-1 adopts an oval curve, which is constructed on... In a rectangular coordinate system Within the second and third quadrants of the plane;

[0096] As shown in Figure 3, the two points that are furthest from the oval curve to its axis of symmetry are the endpoints of the oval curve's symmetry, denoted as . and endpoint and The connecting line is a transition arc. ;

[0097] The oval curve of the end cutting edge 1-1 is tangent to the transition arc of the circumferential cutting edge 1-2 at the end point. Furthermore, the oval curve and the transition arc The connection uses equal curvature, i.e., tangential;

[0098] As shown in Figure 4, the endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is ;

[0099] The equation for the egg-shaped curve is expressed as:

[0100]

[0101] in, Indicates the egg-shaped curve at The coordinate components of the axis, Indicates the egg-shaped curve at The coordinate components of the axis, The major radius of the egg-shaped curve, that is, the egg-shaped curve at... Maximum coordinate range of the axis (radial). The minor radius of the egg-shaped curve, that is, the radius of the egg-shaped curve at... The range of reference coordinates for the axis (axial direction). This is the morphological adjustment coefficient for the egg-shaped curve. Used for correction Axis coordinates, adjusting the smoothness / curvature of the oval shape. , The parameter angles of the egg-shaped curve, i.e., the effective range of parameter angles for the egg-shaped curve. The value is a value in the third quadrant, such that ;

[0102] Based on the above, it should be noted that:

[0103] The parametric equation of a standard ellipse is , The design requires the end cutting edge (egg-shaped curve) and the circumferential cutting edge (transition arc) to meet at the end point. For connections with equal curvature (tangent and identical), the fixed curvature of a standard ellipse cannot meet this requirement; therefore, a shape adjustment coefficient is chosen. The egg-shaped curve correction is achieved by adjusting... Locally altering the curvature of the egg-shaped part in the third quadrant, i.e., the working area of ​​the cutting edge, for example... When, the curve is near (endpoint) The transition curve will be smoother, allowing for precise matching of the curvature of the transition arc and achieving a "seamless connection," thus avoiding roughness on the machined surface due to abrupt changes in curvature during cutting.

[0104] radius of transition arc With tool radius satisfy:

[0105] As shown in Figure 4, the center of the transition arc is... ,straight line arrive The distance between the axes is , making Therefore, the transition arc The coordinates of the center of the circle are ,in, Center axis coordinate values, Center Axis coordinate values;

[0106] Based on the above, it should be noted that:

[0107] The maximum radial dimension of the circumferential cutting edge is the tool radius. Transition arc The maximum coordinates must be equal to arc The maximum value of the coordinates is equal to the center of the circle. coordinates plus radius center coordinates equal to And a straight line arrive Distance of axis And that distance is Pointed Coordinates, therefore, point coordinates equal to The transition arc needs to pass through and Two points, the distance from the center of the circle to both points is 1. Egg balls in The curvature of a point must be equal to the curvature of the transition arc, combined with the center of the circle. , point To obtain the center of the circle coordinates equal to .

[0108] The equation for the transition arc is expressed as:

[0109]

[0110] in, Indicates the transition arc at The coordinate components of the axis, Indicates the transition arc at The coordinate components of the axis, The parameter angle is the transition arc.

[0111] Based on the above, it should be noted that:

[0112] center of transition arc Coordinates are , radius is Parameter angle Let represent the angle between the line connecting a reference direction on the arc to any point on the arc and the center of the arc. Then the coordinates of any point on the arc are... It is expressed in the form of the transition arc equation described above, which is the general form of the parametric equation of an arc.

[0113] center coordinate The core positioning basis for the transition arc position: in Axial direction, center of circle The axis coordinates are Combined with the radius of the transition arc This allows for the maximum arc. Axis coordinates equal to (Consistent with the tool radius) Ensure the transition arc does not exceed the tool's radial range to avoid collision with the workpiece during cutting; Axial direction, center of circle The axis coordinates are It can satisfy the transition arc. , Geometric requirements for two points (from the center of the circle to the center of the circle) , The distance between two points is equal to the radius. It can also adapt to oval curves at the endpoints. The curvature at the point allows for a connection of equal curvature between the two, ultimately achieving a seamless connection between the end cutting edge and the peripheral cutting edge.

[0114] in, This indicates that a point on the arc is relative to the center of the circle. Offset in the axial direction This indicates that a point on the arc is relative to the center of the circle. Offset in the axial direction;

[0115] Parameter angle of transition arc Scope It is determined based on the "start and end points" of the transition arc, and its function is:

[0116] : The starting point of the corresponding arc (The symmetrical endpoints of the egg shape) (overlap), ensuring the arc from Starting from the point, connect to the circumferential blade section;

[0117] : The endpoint of the corresponding arc (Connection point with egg-shaped ball) (overlap), ensuring the arc reaches End of point, connecting to the end of the cutting edge;

[0118] Only keep Range: Avoid the arc exceeding " → The effective connection segment reduces tool material waste while ensuring that the cutting path only covers the working area.

[0119] Based on the above embodiments, the oval-shaped rotating surface is composed of an oval curve and a transition arc. Axis rotation generation:

[0120] Egg-shaped curve Rotating the shaft 360° yields the end-cutting edge rotation surface, the equation of which is:

[0121]

[0122] in, They represent any point on the egg-shaped surface at... axis, axis, The coordinate components of the axis, For the egg-shaped curve The angle of rotation of the axis;

[0123] The end-cutting surface is a variable curvature rotary surface, corresponding to the tip cutting area of ​​the tool head;

[0124] Based on the above, it should be noted that:

[0125] Defined In the coordinate system, The axis is the direction of the milling cutter axis, and any two-dimensional curve (located in) Plane, containing only axis, (axis coordinates) around When generating a 3D surface by rotating the axis 360°, the logic of "cylindrical coordinate transformation" is followed:

[0126] Points on the egg-shaped curve ( ,0, ) around Axis rotation angle Then, its three-dimensional coordinates ( )satisfy:

[0127]

[0128]

[0129]

[0130] Due to the surrounding When the axis rotates, the point reaches The distance between the axes remains constant, only when The change of azimuth angle in a plane needs to be described using trigonometric functions. Coordinate projection in a plane;

[0131] The two-dimensional coordinates of the egg-shaped curve are ( , ), around When the shaft rotates:

[0132] Axial components : Directly follow the egg-shaped curve ,Right now Rotation parallel to The axis and axial coordinate remain unchanged to ensure that the "axial cutting depth" of the end cutting edge is consistent with the original egg-shaped curve;

[0133] radial foundation During rotation, this radial distance remains constant, serving as... The "reference length" of a plane projection is used for calculation. and ;

[0134] Represents the radial coordinates of the egg-shaped curve exist Projection of the axis , Change Coverage In both positive and negative directions of the axis, ensure the complete radial cutting range;

[0135] Represents the radial coordinates of the egg-shaped curve exist The projection of the axis, similarly follows Change Coverage The positive and negative directions of the axis, and Together constitute The "circular trajectory" in the plane corresponds to the rotary cutting path of the tool tip;

[0136] Because the original egg's circular curve is "with a shape adjustment coefficient" "The variable curvature curve", around The rotating surface of the cutting edge formed after the shaft rotates is necessarily a "variable curvature rotating surface". This characteristic is just right for "cutting the tip of complex curved surfaces". By matching the curvature of the workpiece surface with the curvature change of the egg-shaped curve, the cutting impact is reduced.

[0137] Rotate the transition arc around Rotating the axis by 360° yields the transition zone surface, whose equation is expressed as:

[0138]

[0139] in, They represent any point on the transition arc surface at... axis, axis, The coordinate components of the axis, For transition arc The angle of rotation of the axis;

[0140] The connecting area surface is a fixed curvature rotation surface, corresponding to the connecting transition area between the cutting area at the tip of the tool head and the side of the tool holder;

[0141] The cutting edge area and the transition area are smoothly joined along their common boundary to form a complete oval-shaped rotating surface.

[0142] Based on the above, it should be noted that:

[0143] Similarly, the surface equation of the transition zone is based on the transition circular arc. The geometric principle of axis rotation is derived, and the core is to retain the core function of the transition arc—"fixed curvature, connecting the end cutting edge and the circumferential cutting edge"—through "rotational extension":

[0144] The transition arc, as a two-dimensional curve, has the following radial coordinates: , Axial coordinates are , around When the axis rotates, the axial coordinate remains unchanged (the direction of rotation is parallel to the axis). (Axis), ensuring that the equal curvature connection between the transition arc and the oval curve in the axial direction is not disrupted; the radial coordinate serves as the "to" axis. "Fixed distance of axis", through transition arc around Angle of rotation of the axis ( ) respectively in axis, Generate projection components in the axial direction , Ultimately, three-dimensional coordinates are formed. , , );

[0145] Because the original transition arc is a curve with a fixed curvature, around The connecting area surface generated after the shaft rotates is naturally a "frustum-shaped surface with fixed curvature". This characteristic not only ensures the surface flatness when cutting the side of the peripheral cutting edge, but also enables a continuous transition with the variable curvature rotating surface of the end cutting edge at the splicing point, avoiding machining defects caused by surface discontinuity during cutting, and ultimately achieving an integrated functional adaptation of "end cutting tip cutting + peripheral cutting side cutting".

[0146] The splicing of the end-edge rotation surface and the connecting area curved surface has a natural continuity: the end-edge rotation surface is formed by an oval curve. The axis is rotated to generate the surface of the transition zone, which is formed by the transition arc. The axis is rotated to generate the oval curve, while the transition arc and the oval curve are at the endpoints. The point has achieved equal curvature tangency, when the two revolve around When the shaft rotates, the endpoints This will form a "rotation trajectory circle," on which the rotating surface of the end-cutting edge and the curved surface of the connecting area completely coincide, without any gaps or abrupt changes in curvature. Based on this, the tip cutting area corresponding to the end-cutting edge and the connecting area corresponding to the connecting area are spliced ​​together to form a complete curved surface without discontinuities and with continuous curvature. This curved surface is the oval head rotation surface of the oval head milling cutter.

[0147] Based on the above embodiments, as shown in Figure 2, the end cutting part 1-1 is provided with an end cutting front face 3 and an end cutting rear face 5, and the peripheral cutting part 1-2 is provided with a peripheral cutting front face 4 and a peripheral cutting rear face 6.

[0148] S2. Based on the basic surface model of the oval head revolution surface, obtain the surface profile of the oval head revolution surface, and evenly distribute it along the circumferential direction of the milling cutter. Each cutting edge generates a cutting edge profile along a right-hand spiral trajectory at its installation position, and the first rake face and the first flank face are machined according to preset tool angle parameters to form a milling cutter solid model, while simultaneously constructing the complex curved surface to be machined.

[0149] Based on the above embodiments, a complex curved surface to be processed is constructed, and the specific logic is as follows:

[0150] Using the oval-shaped rotating surface as a reference, and centering on the center of the oval-shaped rotating surface, evenly distributed along its circumference. One blade, If the complex curved surfaces of aero-engine blades are to be machined, If machining ordinary mold cavities, ;

[0151] Press 360° / The included angle is used to define the blade mounting positions. The blade profile is generated along the right-hand helical trajectory of each blade mounting position. The parametric equation of the right-hand helical is:

[0152]

[0153] in, For any point on the spiral, axis, axis, The coordinate components of the axis, For spiral winding The rotation angle of the shaft, , For spiral winding The number of revolutions of the axis, The helix angle, ;

[0154] Based on the above, it should be noted that:

[0155] The cutting edge of the milling cutter is a "functional extension" of the oval-shaped rotating surface. Its spatial position must strictly conform to the radial and axial dimensions of the cutter head. If the radial direction of the cutting edge exceeds the range of the cutter head, it will cause collision with the non-machined area of ​​the workpiece during cutting. If the axial direction does not cover the effective cutting length of the cutter head, it will leave a machining blind zone. If the radial / axial dimensions are misaligned with the cutter head, it will damage the overall structural rigidity of the milling cutter.

[0156] The parametric equations for the right-hand helix ensure a perfect dimensional match between the cutting edge and the oval-shaped turning surface through radial and axial constraints. The specific logic is as follows:

[0157] Radial constraint: through and The radial dimension of the fixed blade is aligned with the radial reference of the oval head's rotating surface;

[0158] The core radial reference of the oval head's rotating surface is the "major radius of the oval curve". —Whether it's the rotating surface of the cutting edge or the curved surface of the connecting area, both are based on As the radial dimension reference, in the above equation, and It is a radius of The circle in Parametric equations of a plane From 0 to At any rotation angle All satisfy This means "any point on the blade to..." The distance between the axes is always equal to This constraint directly aligns the radial dimension of the cutting edge with the radial reference of the oval-shaped head's rotating surface. Perfect alignment, preventing the blade from being too coarse radially (greater than) This will not cause collisions with the workpiece, nor will it cause damage due to excessively thin radial diameters (less than 1 mm). This allows the effective cutting area of ​​the oval-shaped head's rotating surface to remain idle, achieving a "gap-free match" between the cutting edge and the radial dimensions of the head.

[0159] Axial constraint: through Control the axial distribution of the cutting edge to cover the effective cutting length of the oval-shaped turning surface;

[0160] The effective axial cutting length of the oval-shaped head's rotating surface is determined by the minor radius of the oval curve. Transition arc center The axial coordinates together determine that the cutting edge must completely cover this range along the axial direction to avoid blind spots in axial machining. In the above equations, Follow Linear variation for precise control of the blade's axial position:

[0161] when hour, , corresponding to the starting position of the axial direction of the cutter head;

[0162] when hour, , corresponding to the axial end position of the cutter head;

[0163] By adjusting and ,let The maximum value exactly matches the maximum axial dimension of the cutter head, such as equal to the egg-shaped curve. The maximum value ensures that the cutting edge completely covers the effective cutting area of ​​the tool head along the axial direction, with no axial machining omissions.

[0164] Based on the above embodiments, the preset tool angle parameters include the rake angle. First rear corner Second rear corner , , , ;

[0165] As shown in Figure 2, chip grooves 7 are pre-reserved between adjacent cutting edges. The first rake face is then machined. With the first back face First rake face With the first back face The equation for the oval transition curve at the connection point is:

[0166]

[0167] in, For any point on the egg-shaped transition curve, axis, The coordinate components of the axis, The transition curves of the egg shape are respectively at In the coordinate system axis, Axis translation amount, The transition curve for the egg-shaped shape is around the origin. The rotation angle, where, The value of and the helix angle Strong association, and must be close to the front corner The value, therefore The scope is: , The parameter angle of the egg-shaped transition curve. , The initial parameter angle of the transition curve, The value of must satisfy two constraints:

[0168] Constraint 1: To be in line with the egg-shaped curve Point parameter angle The transition curve should be aligned to ensure that it starts from the end of the cutting edge and does not overlap with it.

[0169] Constraint 2: with wedge angle Matching, satisfying To avoid the transition curve exceeding the range of the oval head's rotating surface;

[0170] In summary, The scope is: , It is a wedge angle. ;

[0171] Based on the above, it should be noted that:

[0172] The core function of the transition curve is to "connect the first rake face and the first flank face". Since both the first rake face and the first flank face are based on the oval head rotary surface design, the "basic shape" of the transition curve must maintain the same curvature as the oval curve to avoid abrupt curvature changes at the connection point.

[0173] The transition curve must be consistent with the right-hand spiral trajectory of the cutting edge to avoid misalignment between the transition curve and the cutting edge, and it must also be compatible with the tilt posture of the first rake face to ensure that the transition curve can smoothly connect to the first rake face.

[0174] The original coordinates of the transition curve before rotation are set as follows:

[0175] original Axis coordinates: ;

[0176] original Axis coordinates: ;

[0177] Both requirements require circling around the origin. The rotational transformation is achieved by rotating around the origin in a Cartesian coordinate system. The rotation matrix of the angle is:

[0178]

[0179] Based on the rotation matrix, we obtain:

[0180]

[0181]

[0182] Original axis, Substituting the coordinate axes into the equation , ,get:

[0183]

[0184]

[0185] Furthermore, considering the chip groove space requirements between adjacent cutting edges—if only rotational transformation is used, the transition curve may overlap with the flank face of adjacent cutting edges, or the chip groove volume may be insufficient; therefore, superposition is necessary. axis, Translation in the axial direction , The overall position of the transition curve is fine-tuned to ultimately form a complete oval transition curve equation.

[0186] The cutting edge contour conforms to the end cutting edge rake face 3, end cutting edge flank face 5, peripheral cutting edge rake face 4, and peripheral cutting edge flank face 6 of the oval-shaped rotating surface. The first rake face and the first flank face are machined according to the preset tool angle parameters to form a milling cutter solid model containing cutting edge and chip groove, thereby constructing the complex curved surface to be machined.

[0187] Among them, the blade profile conforms to the front cutting face 3, rear cutting face 5, front cutting face 4, and rear cutting face 6 of the end cutting edge of the oval-shaped rotating surface. The specific logic is as follows:

[0188] Define the coordinate range of the front / back face of the end-edge cutting edge and the front / back face of the circumferential cutting edge. The end-edge face is based on the end-edge rotation surface, and the circumferential face is based on the surface of the connecting area. Simultaneously, extract the connection point between the end-edge and circumferential cutting edges. As a benchmark for docking;

[0189] Retrieve the right-hand spiral cutting edge trajectory and align its starting point with the axial starting point of the cutting head. Adjust the number of rotations. Align the axial end of the cutting edge with the maximum axial dimension of the cutting head, ensuring the radial direction of the cutting edge (to) axial distance is ) Consistent with the end cutting edge, in The point matches the cutting edge surface.

[0190] The process involves machining the first rake face and the first flank face according to preset tool angle parameters to form a milling cutter solid model containing cutting edges and chip grooves. The specific logic is as follows:

[0191] Within the preset tool angle parameter range, using the cutting edge as a reference, along the direction perpendicular to the cutting edge, at the rake angle... Machining the rake face of the end cutting edge and the rake face of the peripheral cutting edge, then using the non-cutting side of the cutting edge as a reference, along the direction perpendicular to the machined surface of the workpiece at the first clearance angle. Machining the non-cutting area of ​​the covered end / peripheral cutting edge and in The first back face of the point connection is pressed at the second back angle on its outer side. The second rear angle is machined with a width of 1-2mm to reduce friction;

[0192] Along the circumference of the milling cutter, define a chip groove area between two adjacent cutting edges, with the groove circumference width defined as 360° / The included angle is set, and the bottom of the groove adopts the same curvature parameter as the egg-shaped curve of the end cutting edge. The groove depth is 1 / 4 to 1 / 3 of the radial dimension of the tool head, which ensures sufficient chip removal space and avoids weakening the rigidity of the tool body.

[0193] by With the coordinate system as the reference, in Draw a closed two-dimensional cross-section in a plane. The cross-section must include the oval curve of the end cutting edge, the transition arc of the peripheral cutting edge, the contour of the first rake / rear face after machining, and the contour of the chip groove. Then, draw this two-dimensional cross-section around... The shaft rotates 360° to generate a three-dimensional structure of the end cutting edge, peripheral cutting edge, and an annular chip groove. Finally, the... Each blade is positioned at 360° / The circumferential angle distribution is assembled and integrated with the three-dimensional cutting face and chip groove along the right-hand spiral trajectory to obtain a complete end mill solid model containing the cutting edge and chip groove.

[0194] When constructing a complex surface to be processed, it is necessary to determine the curvature range, radial dimension, and axial dimension of the complex surface. The specific logic is as follows:

[0195] Based on the major radius of the oval curve of the blade tip short radius Morphological adjustment coefficient The curvature range that the oval head's rotating surface can cover is calculated using the curvature formula. The curvature range of the surface to be processed is locked within this range to ensure that the milling cutter can fit the cutting surface.

[0196] With the long radius of the egg-shaped curve For the constraint, set any point on the surface to The maximum distance between axes is less than or equal to To avoid collision between the milling cutter and the workpiece;

[0197] The surface is set to the maximum axial dimension of the tool head. The total height in the axial direction should be less than or equal to this dimension to avoid blind spots in axial machining.

[0198] S3. Adopting parallel to The plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory. The three-dimensional coordinates of each sampling point are extracted. Using the geometric relationship that the egg-shaped rotating surface and the complex curved surface to be processed are tangent at the tool contact point, the tool position trajectory equation is derived and the motion trajectory of the tool position point is obtained by solving it.

[0199] Based on the above embodiments, a parallel The cutting plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory. The three-dimensional coordinates of each point are extracted. The specific logic is as follows:

[0200] By parallel to The planar cutting plane is used to cut the complex curved surface to be processed into layers. Axis coordinates The equation of the cross-sectional plane corresponding to the layer height in CNC machining is: , For the first A cross-section Axis coordinates, i.e., the first axis coordinates The layer height of each cross-section, For the index of the cutting plane, , This represents the total number of cross-sectional planes.

[0201] Based on the above, it should be noted that:

[0202] The complex curved surface to be processed is a three-dimensional shape with variable curvature, making it difficult to directly extract the tool contact trajectory. Therefore, by... Parallel cutting planes can decompose a three-dimensional curved surface into... Each layer has a "two-dimensional intersection line", which transforms the complex spatial trajectory problem into a simple planar curve problem, reducing the computational complexity of toolpath calculation;

[0203] The intersection of the cutting plane and the curved surface is the trajectory of the tool contact point. Any point on the intersection line... The axial coordinates are always It is only necessary to solve this through the surface equation. Value axis, Using the axis coordinates, the complete three-dimensional coordinates of the tool contact point can be quickly obtained.

[0204] Based on the above embodiments, curvature analysis is performed on the complex surface to be processed. The equation of the complex surface to be processed is as follows:

[0205]

[0206] in, This is the equation expression for the complex surface to be processed. For any point on the complex surface to be processed, In coordinate system The coordinate components of the axis The coordinate components of the axis The coordinate components of the axis, These are the first shape control parameters and the second shape control parameters of the complex curved surface to be processed, respectively. This is the matrix transpose.

[0207] Parametric surfaces cannot be directly expressed using simple rectangular coordinate equations; they require... Constructing a mapping relationship between a two-dimensional parameter domain and a three-dimensional surface, such as the surface of an aircraft blade. Corresponding to the "span" of the blade. Corresponding to the "chord direction", by adjusting The range of values ​​is fully covered, encompassing all points on the surface, thus enabling precise positioning of the surface shape.

[0208] Calculate the curvature at any point on the complex surface to be processed. For surface regions where the rate of curvature change is less than the curvature change threshold, the surface is smooth and the curvature is uniform, with small differences in the intersection lines of adjacent cutting planes. To ensure efficiency, the range of values ​​for the distance between cutting planes is [range missing]. For curved surface regions where the rate of curvature change is not less than the curvature change threshold, the surface transitions abruptly and the curvature differences are large, making them prone to processing defects. To ensure accuracy, the range of values ​​for the intersecting plane spacing is [insert range here]. ;

[0209] The rate of curvature change is equal to the curvature difference between adjacent sampling points / sampling point spacing, reflecting the degree of change in surface curvature. The maximum rate of curvature change of the oval curve at the end of the milling cutter is used as the benchmark value, and the threshold of the rate of curvature change is defined as 1.2 times the benchmark value.

[0210] Based on the above embodiments, the intersection of the cutting plane and the complex curved surface to be processed is the tool contact point trajectory. Multiple sampling points are obtained along the tool contact point trajectory at equal intervals to obtain the three-dimensional coordinates of the tool contact point. The three-dimensional coordinate vector of the tool contact point is represented as:

[0211]

[0212] in, The three-dimensional coordinate vector of the knife contact point. For the index of the sampling point, , The number of sampling points, , , The knife contact points are respectively Each sampling point is axis, axis, The coordinate components of the axis, For the first The first shape control parameter for each sampling point For the first The second shape control parameter for each sampling point.

[0213] Based on the above, it should be noted that:

[0214] The tool contact trajectory is the intersection of the cutting plane and the complex curved surface, essentially a continuous and smooth curve. However, CNC machining relies on "discrete point coordinates" to control the milling cutter's movement. The index settings split the continuous trajectory into Each sampling point has three-dimensional coordinates, which become the "target anchor point" for the milling cutter's motion, thus resolving the compatibility contradiction between "continuous surfaces" and "discrete control".

[0215] CNC machining revolves around controlling the movement of the tool position point. This requires inversely deriving the tool position point coordinates from the tool contact point coordinates. The core logic is as follows: the geometric relationship between the tool position point and the tool contact point is fixed by the milling cutter radius and the cutter head shape. Multiple tool contact point sampling points provide crucial support for this derivation. The trajectory tangent direction is calculated using the coordinate difference between adjacent sampling points. The axis coordinates are matched with the layer height of the cutting plane. Finally, based on the geometric characteristic that "the oval-shaped turning surface and the curved surface are tangent at the tool contact point", the tool position trajectory equation is derived, and the complete motion trajectory is obtained.

[0216] Based on the above embodiments, the geometric relationship between the oval-shaped rotating surface and the complex curved surface to be machined at the tool contact point is utilized to derive the tool position trajectory equation and solve for the motion trajectory of the tool position. The specific logic is as follows:

[0217] The tool position point, serving as the center of rotation of the milling cutter, is indirectly determined through the constraint that the milling cutter is tangent to the complex curved surface to be machined. Specifically, it is based on two conditions:

[0218] First, the common point condition: the tool contact point is both on the complex curved surface to be machined and on the milling cutter's rotating surface. The milling cutter's rotating surface only refers to the oval-shaped head rotating surface that participates in the cutting.

[0219] The implicit equation for the milling cutter's revolution surface is:

[0220]

[0221] in, , , For any point on the rotating surface of the milling cutter, axis, axis, The coordinate components of the axis, , , The knife point is located at axis, axis, The coordinate components of the axes;

[0222] Second, the condition of equal normal vectors is that the unit normal vectors of the milling cutter's rotating surface and the complex curved surface to be machined are completely consistent at the tool contact point.

[0223] The unit normal vector of the complex curved surface to be machined at the tool contact point for:

[0224]

[0225] in, The unit normal vectors are respectively in axis, axis, The coordinate components of the axes;

[0226] Taking the partial derivative of the function on the left-hand side of the implicit equation of the surface of revolution, we obtain the gradient vector. :

[0227] in, Implicit function pairs of the surface of revolution axis, axis, First-order partial derivatives of the axial coordinates;

[0228] in:

[0229]

[0230]

[0231]

[0232] The magnitude of the gradient vector for:

[0233]

[0234] Therefore, the unit normal vector of the milling cutter's rotating surface for:

[0235]

[0236] By solving the equations showing the equality of two normal vectors, and substituting the three-dimensional coordinates of the tool contact point, we obtain the three-dimensional coordinates of the corresponding tool position point. The three-dimensional coordinates of the tool position point are expressed as:

[0237]

[0238] in, The knife contact points are respectively at axis, axis, The coordinate components of the axis, For transition parameters, ;

[0239] Based on the above, it should be noted that:

[0240] Solving for the tool position using the "common point condition" and the "equal normal vector condition" is essentially about achieving both a "unique valid solution" and "precise cutting" through dual constraints.

[0241] If only the common point condition is used, there will be an infinite number of tool position points. If only the equal normal vector condition is used, the specific position cannot be determined, and both will produce invalid solutions. The common point condition first ensures that the tool contact point is the actual cutting contact point, and the equal normal vector condition then locks the direction and distance of the tool position point. The combination of the two is used to select the unique tool position point that meets the requirements of "can cut and cut accurately".

[0242] Connect all tool points corresponding to the cutting planes according to the following rules:

[0243] Within the same cross-sectional plane, the first shape control parameter and the second shape control parameter of the complex curved surface to be processed are sorted in ascending order;

[0244] Between different cross-sectional planes, according to the cross-sectional plane Axis coordinates Increasing sort;

[0245] Ultimately, a spiral continuous trajectory is formed that covers the complex curved surface to be processed, which is the motion trajectory of the tool position point.

[0246] Based on the above, it should be noted that:

[0247] The CNC system cannot directly control the movement of the "tool contact point", but can only drive the "tool position point". By solving the tool position point trajectory, the relationship between "tool position point movement → tool contact point conforming to the curved surface for cutting" can be established. When the tool position point moves according to the trajectory, it can ensure that the milling cutter's rotating surface is always tangent to the curved surface at the tool contact point, which avoids overcutting or undercutting and ensures the stability of the cutting contact.

[0248] The complex curved surface to be machined is three-dimensional, and the milling cutter needs to move along a continuous path to completely cover the machining area. When solving the tool position trajectory, it is done by "moving along the same cutting plane". , Sort by different cross-sections "Sorting" integrates discrete tool positions into a spiral continuous trajectory, ensuring that the milling cutter processes the surface from bottom to top and from edge to center without omission, resulting in a smooth transition of the surface and uniform axial spacing. This avoids frequent start-stop or abrupt changes in direction of the milling cutter, reduces machining vibration, and ensures that surface roughness and geometric tolerances meet the standards.

[0249] S4. Associate the motion trajectory of the tool position point and the complex curved surface to be machined, simulate the cutting process of the egg-shaped head rotating surface on the complex curved surface, check for interference and whether the accuracy meets the standard during the process, and adjust the long radius, short radius and shape adjustment coefficient of the egg-shaped curve according to the verification results until the above conditions are met, and complete the overall design of the egg-shaped head rotating surface and the milling cutter.

[0250] 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.

[0251] 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 software, 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.

[0252] 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.

[0253] 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 for machining complex curved surfaces, characterized in that, The milling cutter includes a head (1) and a shank (2). One end of the shank (2) is coaxially and fixedly connected to the head (1). The other end, away from the shank (2), has an oval-shaped rotating surface integrally formed on the outer circumferential surface of the head (1). The design method of the oval-shaped rotating surface includes the following steps: S1. Constructing a three-dimensional rectangular coordinate system and constructing a basic surface model of the oval-shaped rotating surface based on the three-dimensional rectangular coordinate system; S2. Based on the basic surface model of the oval-shaped rotating surface, obtaining the surface profile of the oval-shaped rotating surface, uniformly arranging S cutting edges along the circumferential direction of the milling cutter, generating the cutting edge profile along the right-hand spiral trajectory of each cutting edge installation position, and machining the first front cutting edge according to the preset tool angle parameters. S3. The cross-section plane parallel to the XOY plane intersects with the complex surface to be processed. The resulting intersection line is used as the tool contact point trajectory, and the three-dimensional coordinates of each sampling point are extracted. Using the geometric relationship between the egg-shaped rotating surface and the complex surface to be processed at the tool contact point, the tool position trajectory equation is derived and the motion trajectory of the tool position point is obtained. S4. Based on the motion trajectory of the tool position point, the cutting process of the egg-shaped rotating surface on the complex surface is simulated, and the overall design of the egg-shaped rotating surface and the milling cutter is completed. The head of the cutter (1) includes an end cutting part (1-1) and a peripheral cutting part (1-2). The rotation generatrix of the end cutting part (1-1) adopts an egg-shaped curve. The egg-shaped curve is constructed on In a rectangular coordinate system Within the second and third quadrants of the plane; the two points with the greatest distance from the oval curve to its axis of symmetry are taken as the endpoints of the oval curve's symmetry, denoted as... and endpoint and The connecting line is a transition arc. The oval curve of the end cutting edge (1-1) is tangent to the transition arc of the circumferential cutting edge (1-2) at the end point. Furthermore, the oval curve and the transition arc Use equal curvature connection, i.e., tangent; endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is endpoints and the origin The connecting line is a line segment. line segment and The included angle of the axis is The equation for the egg-shaped curve is expressed as: in, Indicates the egg-shaped curve at The coordinate components of the axis, Indicates the egg-shaped curve at The coordinate components of the axis, The major radius of the oval curve, The short radius of the oval curve, This is the morphological adjustment coefficient for the egg-shaped curve. ， Let be the parameter angle of the egg-shaped curve. Radius of the transition arc With tool radius satisfy: Transition arc The coordinates of the center of the circle are The equation for the transition circle arc is expressed as: in, Indicates the transition arc at The coordinate components of the axis, Indicates the transition arc at The coordinate components of the axis, The parameter angle of the transition arc; the oval head rotation surface is formed by the oval curve and the transition arc. Axis rotation generation: oval curve around Rotating the shaft 360° yields the end-cutting edge rotation surface, the equation of which is: in, They represent any point on the egg-shaped surface at... axis, axis, The coordinate components of the axis, For the egg-shaped curve The angle of axis rotation; the end-edge rotation surface is a variable curvature rotary surface, corresponding to the cutting area at the tip of the tool head; the transition arc is rotated around... Rotating the axis by 360° yields the transition zone surface, whose equation is expressed as: in, They represent any point on the transition arc surface at... axis, axis, The coordinate components of the axis, For transition arc The angle of axis rotation; the connecting area surface is a fixed curvature rotation surface, corresponding to the transition area between the cutting area at the tip of the tool head and the side of the tool holder; the tip cutting area and the transition area are smoothly spliced ​​along their common boundary to finally form a complete oval-shaped rotation surface; the complex surface to be processed is constructed according to the following logic: taking the oval-shaped rotation surface as the reference, and taking the center of the oval-shaped rotation surface as the center, evenly distributed along its circumference. Each blade, arranged in 360° / The included angle is used to define the blade mounting positions. The blade profile is generated along the right-hand helical trajectory of each blade mounting position. The parametric equation of the right-hand helical is: in, For any point on the spiral, axis, axis, Axis coordinate components, For spiral winding The rotation angle of the shaft, ， For spiral winding The number of revolutions of the axis, The helix angle is specified; the preset tool angle parameters include the rake angle, the first clearance angle, and the second clearance angle; a chip groove (7) is reserved between adjacent cutting edges, and the first rake face is machined. With the first back face First rake face With the first back face The equation for the oval transition curve at the connection point is: in, For any point on the egg-shaped transition curve, axis, The coordinate components of the axis, The transition curves of the egg shape are respectively at In the coordinate system axis, Axis translation amount, The transition curve for the egg-shaped shape is around the origin. rotation angle, The parameter angle of the egg-shaped transition curve. ， The initial parameter angle of the transition curve, The wedge angle is used; the cutting edge contour fits the end cutting edge front face (3), end cutting edge back face (5), peripheral cutting edge front face (4) and peripheral cutting edge back face (6) of the oval head rotating surface, and the front and back faces are machined according to the preset tool angle parameters to form a milling cutter solid model containing cutting edge and chip groove, thereby constructing the complex curved surface to be machined.

2. The milling cutter for machining complex curved surfaces according to claim 1, characterized in that, The three-dimensional rectangular coordinate system has the tool center point as the origin. With the direction of the milling cutter axis as The axis is defined as the direction outward from the radial section of the tool holder passing through the origin along the tool radius. Axis, determined by the right-hand rule Three-dimensional rectangular coordinate system of axes 。 3. The milling cutter for machining complex curved surfaces according to claim 1, characterized in that, The end cutting edge (1-1) is provided with a front cutting edge (3) and a rear cutting edge (5), and the peripheral cutting edge (1-2) is provided with a front cutting edge (4) and a rear cutting edge (6).

4. The milling cutter for machining complex curved surfaces according to claim 2, characterized in that, Using parallel to The cutting plane intersects with the complex curved surface to be processed, and the resulting intersection line is used as the tool contact point trajectory, from which the three-dimensional coordinates of each point are extracted. The specific logic is as follows: by parallel to... The planar cutting plane is used to cut the complex curved surface to be processed into layers. Axis coordinates The equation of the cross-sectional plane corresponding to the layer height in CNC machining is: ， For the first A cross-section Axis coordinates For the index of the cutting plane, ， Let be the total number of cutting planes; perform curvature analysis on the complex surface to be machined, and the equation of the complex surface to be machined is: in, This is the equation expression for the complex surface to be processed. For any point on the complex surface to be processed, In coordinate system The coordinate components of the axis The coordinate components of the axis The coordinate components of the axis, These are the first shape control parameters and the second shape control parameters of the complex curved surface to be processed, respectively. This is the matrix transpose; calculate the curvature at any point on the complex surface to be processed. For surface regions where the rate of change of curvature is less than the threshold, the range of values ​​for the intersecting plane spacing is... For surface regions where the rate of curvature change is not less than the curvature change threshold, the range of values ​​for the intersecting plane spacing is: The intersection of the cutting plane and the complex curved surface to be processed is the tool contact point trajectory. Multiple sampling points are obtained along the tool contact point trajectory at equal intervals to obtain the three-dimensional coordinates of the tool contact point. The three-dimensional coordinate vector of the tool contact point is represented as: in, The three-dimensional coordinate vector of the knife contact point. For the index of the sampling point, , The number of sampling points, The knife contact points are respectively Each sampling point is axis, axis, The coordinate components of the axis, For the first The first shape control parameter for each sampling point For the first The second shape control parameter for each sampling point.

5. The milling cutter for machining complex curved surfaces according to claim 4, characterized in that, The method utilizes the geometric relationship of the tangency between the oval-shaped cutting edge's rotating surface and the complex surface to be machined at the tool contact point to derive the tool position trajectory equation and solve for the motion trajectory of the tool position. The specific logic is as follows: The tool position, as the center of rotation of the milling cutter, is indirectly solved through the constraint of the tangency between the milling cutter and the complex surface to be machined, specifically based on two conditions: First, the common point condition, where the tool contact point is both on the complex surface to be machined and on the milling cutter's rotating surface. The milling cutter's rotating surface only refers to the oval-shaped cutting edge's rotating surface participating in the cutting. The implicit equation of the milling cutter's rotating surface is: in, For any point on the rotating surface of the milling cutter, axis, axis, The coordinate components of the axis, The knife point is located at axis, axis, The coordinate components of the axis; secondly, the condition of equal normal vectors: the unit normal vectors of the milling cutter's rotating surface and the complex surface to be machined at the tool contact point are completely identical; the unit normal vector of the complex surface to be machined at the tool contact point... for: in, The unit normal vectors are respectively in axis, axis, The coordinate components of the axes; taking the partial derivatives of the function on the left-hand side of the implicit equation of the surface of revolution to obtain the gradient vector. ： in, Implicit function pairs of the surface of revolution axis, axis, The first-order partial derivatives of the axial coordinates; where: The magnitude of the gradient vector for: Therefore, the unit normal vector of the milling cutter's rotating surface for: By solving the equations showing the equality of two normal vectors, and substituting the three-dimensional coordinates of the tool contact point, we obtain the three-dimensional coordinates of the corresponding tool position point. The three-dimensional coordinates of the tool position point are expressed as: in, The knife contact points are respectively at axis, axis, The coordinate components of the axis, For transition parameters; connect all tool points corresponding to the cutting planes according to the following rules: within the same cutting plane, sort in ascending order according to the first shape control parameter and the second shape control parameter of the complex surface to be machined; between different cutting planes, sort according to the cutting plane... Axis coordinates The process involves ascending sorting to ultimately form a continuous spiral trajectory covering the complex surface to be processed; this trajectory is the motion trajectory of the tool position point.

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