Polishing tool anti-interference calculation system and method for aspheric element
The rotation angle of the cradle shaft and the curvature radius of the polishing head are determined by the surface equation of the aspherical element. The discrete feature point detection method is used to solve the tool path complexity and interference detection problems in five-axis CNC polishing processing, and efficient and accurate anti-interference calculation is achieved.
Patent Information
- Application Number
- CN202510396279.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-31
- Publication Date
- 2025-07-08
AI Technical Summary
In five-axis CNC polishing processing, the complexity of tool paths and the difficulty of interference detection increase, especially when processing complex aspherical components, resulting in high computational complexity and slow detection speed.
The rotation angle of the cradle shaft is determined by the surface equation of the aspherical element, the curvature radius of the polishing head is calculated, the appropriate radial diameter is selected, and the interference point is judged in the tool coordinate system, and discrete feature points are used for interference detection.
It greatly reduces the computational complexity, improves the detection speed, adapts to dynamic changes in five-axis processing, and ensures that the processing process is efficient and accurate.
Smart Images
Figure CN120277837A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of precision machining, and relates to an anti-interference calculation system and method for an aspherical element by a polishing tool. Background Art
[0002] With the development of modern technology, optical elements are increasingly widely used in the fields of military, aerospace, medical equipment, precision instruments, etc., and the requirements for the manufacturing precision and quality of optical elements are also getting higher and higher. The manufacturing process of optical elements usually includes processes such as rough grinding, fine grinding, polishing, and coating. Among them, polishing is the key step to obtain a super-smooth and low-defect-damage optical surface. The polishing process in the manufacturing of optical elements is the core technical link in the field of precision machining. Its essence is to achieve atomic-level surface quality control through nano-level material removal. This process not only determines the final surface shape accuracy of the element, but also directly affects its optical performance and service life.
[0003] With the surging demand for high-precision complex curved surface elements in modern optics, aerospace and other fields, five-axis CNC machining technology is gradually becoming the core process of precision manufacturing with its unique motion flexibility and processing adaptability. Compared with traditional three-axis machining, five-axis machine tools achieve dynamic adjustment of the relative pose between the tool and the workpiece by introducing two rotational degrees of freedom (usually the A-axis and the C-axis), providing the possibility for machining continuous and smooth free-form surfaces, deep cavity structures, and steep sidewalls. However, this technological upgrade has also brought unprecedented technical challenges.
[0004] In five-axis machining, the tool path needs to consider the coordinated motion of the translational axes (X / Y / Z) and the rotational axes (A / C) simultaneously. The spatial trajectory of the tool center point (TCP) is no longer a simple three-dimensional Cartesian coordinate function, but a non-linear mapping relationship strongly coupled with the rotational axis angles. This coupling causes the tool posture to change in real time, and the linear interpolation strategy in traditional three-axis machining fails. More complex spline interpolation or NURBS curve fitting techniques must be adopted. At the same time, to avoid motion singularities (such as gimbal lock), it is necessary to optimize the motion range of the rotational axes, which increases the difficulty of numerical control machining motion simulation calculation and tool interference inspection, especially when machining the surface of extremely complex parts. Therefore, in order to ensure high-efficiency and high-quality machining on a five-axis CNC polishing machine tool, it is necessary to establish an anti-interference calculation model for an aspherical element by a toroidal tool. Summary of the Invention
[0005] Aiming at the problems existing in the prior art, the present invention provides an anti-interference calculation system and method for an aspherical element by a polishing tool, which greatly reduces the calculation complexity and improves the detection speed.
[0006] The present invention is realized through the following technical solutions: An anti-interference calculation method for an aspherical element by a polishing tool, including, Determine the rotation angles of the cradle axis in the x-axis and z-axis directions according to the aspherical element surface equation and , and obtain the transformed aspherical equation; Calculate the spatial curvature according to the transformed aspherical equation, obtain the maximum curvature of the aspherical element, and thus obtain the curvature radius of the polishing head; Match and select the radial diameter of the polishing head according to the curvature radius of the polishing head; Based on the selected radial diameter of the polishing head, transform the characteristic points of the machining surface into the tool coordinate system and determine whether there are interference points; if there are interference points, select the curvature radius of the polishing arc according to the interference points and the tool diameter .
[0007] Preferably, the specific process of obtaining the transformed aspherical equation is: Set the origin of the aspherical element surface equation , and multiply the rotation matrix left by the origin to obtain the coordinates Z under the rotation angle of the machine tool coordinate system ; Then multiply the coordinates by the rotation matrix left to obtain the rotation angle X of the cradle axis around the axis, and obtain the coordinates X under the rotation angle of the machine tool coordinate system ; Substitute the coordinates into the aspherical element surface equation to obtain the transformed aspherical equation.
[0008] Preferably, the expression of the transformed aspherical equation is:
[0009] In the formula: is the rotation angle of the cradle axis around the Z axis, is the rotation angle of the cradle axis around the X axis.
[0010] Preferably, to calculate the spatial curvature of the transformed aspherical equation, specifically: By calculating the x and yThe partial derivatives are taken to obtain the tangent vector and the normal vector, and then the definition of spatial curvature is used for calculation. The expression for the spatial curvature k of the aspherical element is: ; In the formula: n is the normal vector, is z the x second-order partial derivative of is z the x and y second-order mixed partial derivative of is z the y second-order partial derivative of, which is used to describe the twisting characteristics of the surface in different directions.
[0011] Preferably, the maximum curvature of the aspherical element is obtained to acquire the curvature radius of the polishing head, specifically: The point on the surface of the aspherical element with the maximum curvature, that is, the point with the minimum curvature radius, is calculated through the spatial curvature k of the aspherical element. Then, the curvature radius of the polishing tool needs to satisfy: the curvature radius of the polishing tool is less than the reciprocal of the maximum curvature of the spherical element, that is, the minimum curvature radius of the aspherical element. The expression is: , = ; In the formula: R c is the curvature radius of the polishing tool, k max is the maximum curvature of the spherical element, is the minimum curvature radius of the aspherical element.
[0012] Preferably, the radial diameter of the polishing head is selected according to the curvature radius of the polishing head, specifically: If the minimum curvature radius of the aspherical element is , the radial diameter of the selected polishing head ranges from to for the spherical surface polishing head.
[0013] Preferably, in the polishing tool coordinate system, let the coordinates of the feature point Q be , and the data of the feature point Q is transformed from the machine tool coordinate system to the polishing tool coordinate system for representation; According to the different combined parts of the polishing tool coordinate system, the coordinate values Q of the feature point are divided into two segments for discrimination, and then the diameter of the polishing tool is selectedD With the arc curvature radius ; Characteristic point Q Coordinate value of Divided into two segments including the arc polishing head XOY Extension part, denoted as U1 Segment and the polishing tool housing XOY Extension part, denoted as U2 Segment ； When the characteristic point Q Is in Within the range of the segment, it is divided into two cases: the polished arc part And the tool housing part ; When the characteristic point Q Involves the housing part Then there is no interference; When the characteristic point Q Involves the housing part The polishing tool interferes; When the characteristic point Q Is in Within the range of the segment, then when the distance between the characteristic point Q and the Axis of the polishing tool coordinate system is less than the radius of the polishing tool, the polishing tool interferes; Otherwise, there is no interference of the polishing tool.
[0014] Preferably, when the characteristic point Q Involves the housing part The polishing tool interferes, that is, it satisfies:
[0015] Wherein, Is the thickness of the arc polishing pad under the polishing tool in the Direction of the machine tool coordinate system ; Is the curvature radius of the arc polishing pad; Is the diameter of the polishing tool; Is the margin from the edge of the arc polishing pad at the bottom of the polishing tool to the edge of the tool; Is the tool contact point The set of lens surface characteristic points in the lower area ; Is the projection area of the non-spherical surface under the plane of the tool coordinate system ; Preferably, when the characteristic point Q Is in Within the range of the segment, then when the characteristic point Q to When the distance between the axes is less than the radius of the polishing tool, interference of the polishing tool occurs, that is, it satisfies:
[0016] Otherwise, there is no interference of the polishing tool; Among them, is the diameter of the polishing tool; are the coordinates of the feature points Q respectively.
[0017] An anti-interference calculation system of a polishing tool for an aspherical element includes An aspherical equation acquisition module, which is used to determine the rotation angles and of the cradle axis in the x-axis and z-axis directions according to the aspherical element surface equation, and obtain the transformed aspherical equation; A polishing head curvature radius acquisition module, which is used to calculate the spatial curvature according to the transformed aspherical equation, obtain the maximum curvature of the aspherical element, and thus obtain the polishing head curvature radius; A radial diameter acquisition module of the polishing head, which is used to match and select the radial diameter of the polishing head according to the polishing head curvature radius; A judgment module, which is used to transform the feature points of the machining surface into the tool coordinate system and judge whether there are interference points; if there are interference points, select the polishing arc curvature radius according to the interference points and the tool diameter . Compared with the prior art, the present invention has the following beneficial technical effects: This paper proposes an anti-interference calculation method for a five-axis CNC polishing tool for an aspherical element, that is, first transform the coordinates of the machined surface type to obtain a suitable cradle deflection angle, and then discretize the machining surface into a series of surface feature points. Whether there is tool interference can be judged by whether the feature points enter the inside of the tool surface, which improves the efficiency of interference detection. This anti-interference calculation method has significant advantages compared with traditional interference detection methods. Traditional interference detection usually requires detailed spatial simulation of the entire machining area, with a large amount of calculation and time consumption. The method of interference detection by discretizing feature points proposed in this paper greatly reduces the calculation complexity and improves the detection speed. At the same time, considering various dynamic change factors in five-axis CNC machining, this method can adapt to changes under different machining conditions and ensure that each step in the machining process is in an efficient and accurate state. Description of the Drawings
[0018] Figure 1 is a schematic diagram of the overall polishing CNC machine tool; Figure 2 is the structure diagram and exploded view of the polishing tool; Figure 3It is a schematic diagram of the interference of the polishing tool; Figure 4 It is a schematic diagram of the trajectory of the polishing head; Figure 5 It is a flow chart for anti-interference; In the attached drawings, 1 is the Y-axis moving platform; 2 is the Z-axis moving platform; 3 is the cradle turntable; 4 is the X-axis moving platform; 5 is the polishing tool; 6 is the polishing head housing; 7 is the arc-shaped polishing pad; 8 is the clamping ring; 9 is the polishing layer; 10 is the elastic layer. Specific embodiments
[0019] The following further elaborates on the present invention in combination with specific embodiments, which is an explanation rather than a limitation of the present invention.
[0020] In order to enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.
[0021] The following further describes the present invention in detail with reference to the drawings: As Figure 1 shown, a five-axis cradle-type CNC polishing machine tool is used for the polishing and trimming of aspherical elements; specifically, for the in-situ trimming device of the cup-shaped grinding wheel, a machine tool capable of realizing three-way movement in the X, Y, and Z directions is adopted. At the same time, the machine tool can realize tool rotation along the Y-axis direction, and it also includes a moving platform that can rotate in an arc and rotate self-reliantly along the plane where the Y-axis is located; the present invention adopts a five-axis cradle-type CNC machine tool, including a Y-axis moving platform 1, a Z-axis moving platform 2, an X-axis moving platform 6, and a turntable 3. The turntable 3 can perform arc-shaped operation within the plane where the Y-axis is located; a rotatable machine tool tool is fixed on the Y-axis moving platform 1, and the aspherical element to be trimmed is clamped on the machine tool cradle. The specific anti-interference calculation method for the arc-shaped tool of the five-axis polishing machine tool for aspherical elements includes the following steps: Step 1): For a five-axis polishing machine tool for polishing aspherical elements, the five axes of the machine tool are the X, Y, Z, A, and C axes respectively, and the A and C axes are controlled by the cradle. As the polishing machine tool is Figure 1 shown, since the structure of the polishing tool is a cylindrical metal with an arc-shaped polishing head below, the structure diagram of the polishing tool is Figure 2 shown. During its processing, it is prone to collision interference, so it is necessary to establish a calculation method for selecting and placing the interference of the polishing tool. According to the surface shape of the aspherical element to be polished select the polishing machine tool cradle at x , zRotation angle in the and . For the polishing machining trajectory, the selection principle is that the tool curvature is selected to be greater than the maximum curvature of the quadratic aspheric equation. Since the posture of the polishing tool is always parallel to the Z axis of the machine tool base coordinate system, it is necessary to select the rotation angle of the cradle in the x , z direction before machining to achieve the smoothness of the machining process. Let the point on the lens be and . First, the cradle rotates around the axis by the rotation angle Z to obtain the new coordinates in the machine tool coordinate system, that is, , namely left-multiplying the rotation matrix : (1) The new coordinates in the machine tool coordinate system are: (2) Substitute the new coordinates into to obtain the new equation: (3) Then rotate the cradle around the X axis by the rotation angle to obtain the new coordinates in the machine tool coordinate system, that is, left-multiplying the rotation matrix : (4) The new coordinates in the machine tool coordinate system are: (5) Substitute the new coordinates into the equation to obtain the transformed aspheric equation: (6) For the space curve given by the implicit function of the aspheric element surface , it is first necessary to convert it into the form of a parametric equation. The parametric equation uses two independent parameters ( x , y ) to describe all the three-dimensional coordinates of the surface. Select x and y as parameters, that is: (7) Called the parametric equation or parametric representation of the surface, calculate with respect to x and y partial derivatives to obtain the tangent vector and the normal vector, and then calculate using the definition of curvature. Calculate with respect to x and y partial derivatives: (8) is the first-order partial derivative of x with respect to is the first-order partial derivative of y with respect to and cross product to obtain the normal vector n : (9) n The direction of
[0022] indicates the "outward" or "inward" orientation of the surface at that point. Calculate x with respect to y and (10) Calculate , and dot product with the normal vector n to obtain the numerator of the curvature: (11) is z the second-order partial derivative of x with respect to is z the second-order mixed partial derivative of x and y with respect to is z the second-order partial derivative of y with respect to
[0023] Calculate the denominator of the curvature, which is the cube of the magnitude of the normal vector n : (12) is the magnitude of the normal vector n
[0024] Finally, substitute the numerator and denominator into the curvature formula: (13) By calculation, the point with the maximum surface curvature of the aspherical element, that is, the point with the minimum curvature radius, can be obtained. Then, the curvature radius of the polishing head needs to meet the following conditions: (14) Thus, the cradle rotation angle for the machining of the aspherical element can be obtained and .
[0025] Step 2): Since the curvature of the aspherical element to be trimmed usually varies from the center to the edge, the size of the polishing head needs to match the curvature first. In the area where the curvature changes greatly, a smaller polishing head can be selected to better adapt to different curvatures. If the curvature change is small, using a larger polishing head can improve the polishing efficiency. To meet the requirements of both polishing efficiency and curvature adaptation, if the minimum curvature radius of the aspherical element is , select a toroidal polishing head with a radial diameter ranging from to .
[0026] Step 3): As shown in Figure 4 , a tool coordinate system can also be defined at the cutter contact points (CC points) , and the directions of each axis are the same as those of the machine tool base coordinate system. To simplify the interference model, the interference analysis is carried out with the tool surface with a relatively regular shape as the reference. After the machining surface is discretized, the surface shape is represented by a set of feature points. The original data of these feature points are all represented in the machine tool coordinate system . Therefore, the feature point data must be transformed from the machine tool coordinate system to the tool coordinate system for representation .
[0027] Whether the polishing tool interferes with the machining surface can be determined by whether the discriminant feature point Q enters the interior of the tool surface. As shown in Figure 3 , the position relationship between the tool and the machining surface during the machining of the polishing tool is shown. In the tool coordinate system, let the coordinates of the feature Figure 3 Q be . According to the different combined parts of the tool coordinate system, the coordinate value Z of the feature point Q Q is divided into 2 segments. The feature point Q is discriminated, and its feature area is divided into two segments according to the axis, which are the toroidal polishing head XOYExtension part U1 With the polishing tool housing XOY Extension part U2 The discrimination is carried out as follows: (1) When the feature point Q is within the range of section, there are two cases: the polished arc part and the tool housing part . When the feature point involves the housing part , there is no interference. When the feature point involves the housing part , the tool interferes, that is, it satisfies: (15) Among them, is the thickness of the arc polishing pad under the tool in the coordinate system direction; is the radius of curvature of the arc polishing pad; is the diameter of the polishing tool; is the margin from the edge of the arc polishing pad at the bottom of the polishing tool to the edge of the tool; is the projection area of the tool on the aspherical surface in the plane of the tool coordinate system; is the tool contact point under the area set of lens surface feature points.
[0028] (2) When the feature point Q is within the range of section, then when the distance between the feature point Q and the axis is less than the tool radius, tool interference occurs, that is, it satisfies: (16) Otherwise, there is no tool interference.
[0029] The surface feature points that interfere with the polishing tool coordinate system are called interference points. The polishing head size is selected according to the above method based on the swung lens surface shape, that is, the radius of curvature of the polished arc .
[0030] The cradle swing angle and the entire polishing head size can be integrated into industrial software, and its process is as Figure 5 shown.
[0031] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation of the present invention.
[0032] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.
[0033] In the present invention, unless otherwise clearly specified and defined, the terms "mounted", "connected", "coupled", "fixed", etc. should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or integrated; it can be a mechanical connection, an electrical connection, or a communication connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. When a component is referred to as "fixed to" another component, it can be directly on the other component or there may also be an intermediate component. When a component is considered to be "connected" to another component, it can be directly connected to the other component or there may be an intermediate component at the same time. When a component is considered to be "disposed on" another component, it can be directly disposed on the other component or there may be an intermediate component at the same time.
[0034] In the present invention, unless otherwise clearly specified and defined, the first feature being “above” or “below” the second feature may include direct contact between the first and second features, or may include the situation where the first and second features are not in direct contact but in contact through additional features therebetween. Moreover, the first feature being “above”, “over” and “on top of” the second feature includes that the first feature is directly above and obliquely above the second feature, or merely means that the horizontal height of the first feature is higher than that of the second feature. The first feature being “below”, “beneath” and “underneath” the second feature includes that the first feature is directly below and obliquely below the second feature, or merely means that the horizontal height of the first feature is lower than that of the second feature.
[0035] It should be understood that when used in this specification and the appended claims, the terms “comprises” and “comprising” indicate the presence of the described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their groups.
[0036] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this invention belongs. The terms used in the description of the present invention herein are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term “and / or” as used herein includes any and all combinations of one or more of the related listed items.
[0037] The above are only the preferred embodiments of the present invention and do not impose any formal limitations on the present invention; any person of ordinary skill in the art can smoothly implement the present invention according to what is shown in the drawings of the specification and the above description; however, any equivalent changes, made by those who are familiar with the technology in the technical field of the present invention within the scope of the technical solution of the present invention and by using the technical content disclosed above for a little modification, embellishment and evolution, are all equivalent embodiments of the present invention; at the same time, any equivalent changes, made according to the essential technology of the present invention to the above embodiments for modification, embellishment and evolution, etc., still fall within the protection scope of the technical solution of the present invention.
[0038] The above are only the preferred embodiments of the present invention and do not impose any formal limitations on the present invention; any person of ordinary skill in the art can smoothly implement the present invention according to what is shown in the drawings of the specification and the above description; however, any equivalent changes, made by those who are familiar with the technology in the technical field of the present invention within the scope of the technical solution of the present invention and by using the technical content disclosed above for a little modification, embellishment and evolution, are all equivalent embodiments of the present invention; at the same time, any equivalent changes, made according to the essential technology of the present invention to the above embodiments for modification, embellishment and evolution, etc., still fall within the protection scope of the technical solution of the present invention.
Claims
1. An anti-interference calculation method for an aspherical element by a polishing tool, characterized in that including Determine the rotation angles of the cradle axis in the x-axis and z-axis directions according to the aspheric element surface equation and , and obtain the transformed aspheric equation Calculating the spatial curvature according to the converted aspheric equation to obtain the maximum curvature of the aspheric element, thereby obtaining the curvature radius of the polishing head; Selecting the radial diameter of the polishing head according to the matching of the curvature radius of the polishing head; Based on the radial diameter of the selected polishing head, the characteristic points of the machined surface are transformed from the machine tool coordinate system to the polishing tool coordinate system to determine whether there are interference points; if there are interference points, the curvature radius of the polishing arc is selected according to the interference points and the polishing tool diameter .
2. The anti-interference calculation method for a polishing tool for aspherical elements according to claim 1, characterized in that The specific process of obtaining the converted aspheric equation is as follows: Set the origin of the aspherical element surface equation , passing through the origin Pre-multiply by the rotation matrix , to obtain the machine tool coordinate system Z Axis rotation angle The coordinates under ; Multiply the coordinates on the left by the rotation matrix , to obtain the coordinates of the cradle axis rotated by an angle X about the axis, and the coordinates in the machine tool coordinate system X rotated by an angle are obtained ; Substitute the coordinates into the aspheric surface equation , and obtain the transformed aspheric equation.
3. The anti-interference calculation method of a polishing tool for aspherical elements according to claim 2, characterized in that The converted aspheric equation, the expression is: In the formula: is the rotation angle of the cradle shaft around Z axis, is the rotation angle of the cradle shaft around X axis.
4. The anti-interference calculation method of a polishing tool for aspherical elements according to claim 1, characterized in that Calculating the spatial curvature of the converted aspheric equation, specifically: By calculating the partial derivatives of the aspheric equation with respect to x and y , the tangent vector and the normal vector are obtained, and then by using the definition of spatial curvature for calculation, the expression for the spatial curvature k of the aspheric element is: ； Where: n is the normal vector, is z the x second-order partial derivative of is z the x and y second-order mixed partial derivative of is z the y second-order partial derivative of, used to describe the twisting characteristics of the surface in different directions.
5. A method for anti-interference calculation of a polishing tool for aspherical elements according to claim 4, characterized in that Obtaining the maximum curvature of the aspheric element, thereby obtaining the curvature radius of the polishing head, specifically: Calculating the point with the maximum surface curvature of the aspheric element through the spatial curvature k of the aspheric element, that is, the point with the minimum curvature radius, then the curvature radius of the polishing tool needs to meet: the curvature radius of the polishing tool is less than the reciprocal of the maximum curvature of the spherical element, that is, the minimum curvature radius of the aspheric element, the expression is: ， = ； Wherein: R c is the curvature radius of the polishing tool, k max is the maximum curvature of the spherical element, is the minimum curvature radius of the aspherical element.
6. The anti-interference calculation method for a polishing tool for aspherical elements according to claim 1, characterized in that Selecting the radial diameter of the polishing head according to the matching of the curvature radius of the polishing head, specifically: If the minimum radius of curvature of the aspherical element is , then select a toroidal polishing head with a radial diameter in the range of to .
7. The anti-interference calculation method of a polishing tool for aspherical elements according to claim 1, characterized in that Transforming the characteristic points of the machined surface into the tool coordinate system to judge whether there are interference points, the specific process is: In the polishing tool coordinate system, let the characteristic point Q have the coordinate of , and the data of the characteristic point Q is transformed from the machine tool coordinate system to the polishing tool coordinate system for representation; According to different combined parts of the polishing tool coordinate system, the coordinate values Q of the feature points are discriminated in two segments, and then the diameter of the polishing tool D and the radius of curvature of the arc ; Feature points Q Coordinate values Are divided into two segments including an arc polishing head XOY Extension part, denoted as U1 Segment and the polishing tool housing XOY Extension part, denoted as U2 Segment ； When the feature point Q is in the range of the segment, it is divided into two cases: the polished arc part and the tool housing part ; When the feature points Q involve the housing part no interference occurs; When the feature point Q involves the housing part the polishing tool interferes; When the feature point Q is in section range, when the distance between the feature point Q and the axis of the polishing tool coordinate system is less than the radius of the polishing tool, interference of the polishing tool occurs; Otherwise, there is no interference of the polishing tool.
8. A method for anti-interference calculation of a polishing tool for aspherical elements according to claim 7, characterized in that, When the feature point Q involves the housing part the polishing tool interferes, that is, it satisfies: Among them, is the thickness of the arc polishing pad under the polishing tool in the direction of the machine tool coordinate system ; is the radius of curvature of the arc polishing pad; is the diameter of the polishing tool; is the margin from the edge of the arc polishing pad at the bottom of the polishing tool to the edge of the tool; is the set of characteristic points on the lens surface in the area under the tool contact point ; is the projection area of the non-spherical surface under the plane of the tool coordinate system . 9. A method for anti-interference calculation of a polishing tool for aspherical elements according to claim 7, characterized in that, When the feature point Q is within the range of the segment, when the distance between the feature point Q and the axis is less than the radius of the polishing tool, interference of the polishing tool occurs, that is, it satisfies: Otherwise, there is no interference of the polishing tool; Among them, is the diameter of the polishing tool; are respectively the characteristic points Q coordinates.
10. An anti-interference calculation system of a polishing tool for an aspheric element, characterized in that The aspherical equation acquisition module is used to determine the rotation angles of the cradle axis in the x-axis and z-axis directions according to the aspherical element surface equation and , and obtain the converted aspherical equation; A curvature radius acquisition module of the polishing head, which is used to calculate the spatial curvature according to the converted aspheric equation to obtain the maximum curvature of the aspheric element, thereby obtaining the curvature radius of the polishing head; A radial diameter acquisition module of the polishing head, which is used to select the radial diameter of the polishing head according to the matching of the curvature radius of the polishing head; A judgment module is configured to transform the feature points of the machined surface into the tool coordinate system and determine whether there are interference points. If there are interference points, the polishing arc curvature radius is selected based on the interference points. and the tool diameter .