4+1 axis spiral grinding method for large aperture optical complex curved surface

Abstract

The application discloses a large-diameter optical complex curved surface 4+1-axis spiral grinding method, and mainly solves the problems of complicated process, limited modeling precision, poor adaptability, low processing efficiency and uneven surface quality of the existing grinding method. The grinding method mainly comprises the following steps: step 1, multi-coordinate system construction and off-axis aspheric surface mathematical modeling; step 2, non-spherical surface space discrete coordinate generation; step 3, double-mode adaptive discrete spiral machining track planning; step 4, cutter location point calculation and coordinate system conversion; and step 5, 4+1-axis linkage grinding control. The grinding method has the advantages of high modeling precision, simple process, synergistic improvement of grinding efficiency and surface quality, high multi-axis linkage coordinate mapping precision, strong engineering practicability and easy popularization.

Description

Technical Field

[0001] This invention relates to a grinding method, specifically a 4+1 axis helical grinding method for large-diameter optical complex curved surfaces. Background Technology

[0002] The current mainstream technical approach first involves creating a 3D CAD model of the optical element in commercial software such as Siemens NX. For off-axis aspherical surfaces, it is usually necessary to first perform Taylor expansion, rotation, and truncation of the parent mirror equation to model it. Then, CAM software is used for toolpath planning to generate machining trajectories such as grids, rings, or spirals. This process is not only lengthy and requires a high level of expertise, but also requires a constant feed rate.

[0003] Chinese patent CN103331671A discloses a point-line envelope grinding method for medium and large aperture aspherical optical elements. Although it also uses a discretization method for mathematical equations, the grinding trajectory is a meridional section that converges on the aspherical surface. Then, using the meridional section, the aspherical surface is rotated around the central axis of the optical element. This method can only process coaxial centrally symmetric aspherical surfaces and cannot process more complex asymmetric aspherical surfaces.

[0004] Chinese patent CN110340737A discloses a grinding tool path planning method based on multi-axis linkage with large off-axis distance. This method first requires tangenting the mirror blank to the center point of the rotary table, then connecting the tangent point to the center of the mirror blank, using the off-axis distance to be machined as the distance, to determine the origin of the coordinate system for the aspherical surface to be machined. Then, using the origin of the coordinate system of the aspherical surface to be machined as the center, the surface of the aspherical surface to be machined is divided into several concentric arcs of unequal radii, and these trajectories are connected end-to-end in an S-shape to form an S-shaped machining trajectory. However, this method is relatively complex to operate, can only use grid-shaped machining trajectories, and is relatively inefficient.

[0005] In summary, the existing technology has the following problems:

[0006] 1. Cumbersome process: It relies on multiple software programs, making the operation complex, the process preparation cycle long, and the efficiency low.

[0007] 2. Limited modeling accuracy: The modeling process of off-axis aspherical surfaces introduces mathematical approximations and multiple coordinate transformations, which can easily lead to model errors and affect the final machining accuracy;

[0008] 3. Poor adaptability: For optical elements with different apertures or surface shapes, remodeling is required, resulting in insufficient flexibility;

[0009] 4. Low processing efficiency: The grid-shaped machining trajectory is limited by the linear axis feed speed of the machine tool, resulting in low processing efficiency; the circular machining trajectory requires frequent tool feed and retraction, which is not suitable for grinding continuous curved surfaces;

[0010] 5. Uneven surface quality: The surface roughness of the ground surface increases with the increase of the grinding radius. Grinding at a constant feed rate results in poor surface roughness consistency, which increases the difficulty of subsequent polishing. Summary of the Invention

[0011] The purpose of this invention is to solve the problems of cumbersome process, limited modeling accuracy, poor adaptability, low processing efficiency and uneven surface quality of existing grinding methods, and to provide a 4+1 axis helical grinding method for large-diameter optical complex curved surfaces.

[0012] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0013] A 4+1 axis helical grinding method for large-diameter optical complex curved surfaces, characterized by the following steps:

[0014] Step 1: Construction of Multi-Coordinate Systems and Mathematical Modeling of Off-Axis Aspherical Surfaces

[0015] Establish a global optical coordinate system, an off-axis mirror local coordinate system, and a machine tool coordinate system. Based on the standard aspherical equations in the global optical coordinate system, construct a rotationally symmetric aspherical mathematical model. Then, obtain the off-axis aspherical mathematical model in the local coordinate system through coordinate translation and Givens rotation transformation of the off-axis angle.

[0016] Step 2: Generation of Discrete Coordinates in Aspherical Space

[0017] Based on the mathematical model of off-axis aspherical surfaces, discrete coordinates of aspherical space are directly generated through numerical calculation.

[0018] Step 3: Dual-modal adaptive spiral trajectory planning

[0019] Based on the Archimedes plane spiral curve equation, a dual-modal adaptive discrete spiral machining trajectory with an outer equal arc step size and a central equal angle step size is designed to obtain the plane spiral points; further, the plane spiral points are mapped to the aspherical space discrete coordinates generated in step 2 through bilinear interpolation to obtain the discrete surface spiral trajectory points.

[0020] Step 4: Tool position point calculation and coordinate system transformation

[0021] The finite difference method is used to solve for the normal vector at the discrete surface spiral trajectory point generated in step 3. The tool position spatial coordinates are calculated in combination with the grinding tool radius. Then, the tool position spatial coordinates are converted into C-axis linkage machining trajectory coordinates through a pre-constructed rotation matrix.

[0022] Step 5, 4+1 axis linkage grinding control

[0023] A post-processing model for a vertical oscillating machine tool is constructed. This model compensates for the displacement oscillation of the X and Z linear axes caused by the oscillation of the A oscillating axis. The model is then superimposed with the C rotary axis linkage machining trajectory coordinates obtained in step 4 to obtain the complete motion coordinates in the machine tool coordinate system. The grinding feed trajectory is controlled according to the complete motion coordinates. A pre-constructed C rotary axis variable feed linear interpolation strategy with low speed on the periphery and high speed on the center is adopted to adjust the grinding feed speed in real time, thereby realizing 4+1 axis helical grinding of large-diameter optical complex curved surfaces.

[0024] Furthermore, in step 1, the expression for the rotationally symmetric aspherical mathematical model is:

[0025] ;

[0026] In the formula: radial coordinates At the height of the arrow, , and These are the X-axis and Y-axis coordinates in the global optical coordinate system, respectively. For vertex curvature, , The vertex radius of curvature; It is the conic constant; These are higher-order coefficients for aspherical surfaces; The order of the higher-order terms;

[0027] The translation formula used for coordinate translation is:

[0028] ;

[0029] In the formula: , and These are the intermediate coordinates after translation; Off-axis quantity; The Z-axis coordinate in the global optical coordinate system; The center sagitta of the off-axis mirror;

[0030] When performing the Givens rotation transformation around the off-axis mirror, the coordinate transformation formula used for rotation about the X' axis in the local coordinate system of the off-axis mirror is as follows:

[0031] ;

[0032] ;

[0033] In the formula: , and These are the coordinates in the local coordinate system of the off-axis mirror; It is the off-axis angle; and Radial coordinates and radial coordinates The height of the arrow at the location; The upper limit of the radial coordinate; This represents the lower limit of the radial coordinate.

[0034] Furthermore, in step 3, the formula for calculating the discrete point helical radius of the dual-modal adaptive discrete helical machining trajectory is as follows:

[0035] ;

[0036] In the formula: Located at the polar angle discrete points of location The corresponding polar radius; Located at the polar angle discrete points of location The corresponding polar radius; To specify the helix pitch; For the first Global increment of discrete points in the layer. = ; For the rotation period, ; ;j ; This represents the total number of spiral rotations from the center to the edge. , The radius of the outer circle of the aspherical aperture; Let be the number of discrete points in each spiral trajectory. ; For discrete points Polar angle increment;

[0037] discrete points Polar angle increment satisfy:

[0038] ;

[0039] In the formula: Specify the angle step size; To specify the angle step size corresponding to the arc step size, ; Specify the arc step size;

[0040] The dual-modal adaptive discrete spiral machining trajectory is as follows:

[0041] ;

[0042] By mapping the planar spiral points to the discrete coordinates of the aspherical space generated in step 2 using bilinear interpolation, the discrete surface spiral trajectory points are obtained. The interpolation equation is:

[0043] ;

[0044] In the formula: For discrete points The arrow is high; For discrete points Distance-based weighting coefficients; For discrete points At the point of elevation, discrete point For discrete points The neighboring point.

[0045] Furthermore, in step 4, when using the finite difference method to solve for the normal vector at the point of the discrete surface spiral trajectory, the central difference is applied to the internal points and the one-way difference is applied to the boundary points.

[0046] When applying central difference to interior points, the formula for calculating partial derivatives is as follows:

[0047] ;

[0048] When applying one-way difference to boundary points, the formula for calculating partial derivatives is as follows:

[0049] Left boundary: Right boundary: Upper boundary: Lower boundary: ;

[0050] Tool position spatial coordinates The calculation formula is:

[0051] ;

[0052] ;

[0053] By pre-constructing the machine tool coordinate system Rotation matrix of axis Convert the tool position spatial coordinates into C-axis rotary axis linkage machining trajectory coordinates. , ;

[0054] In the formula: For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; for The total number of discrete points in the direction; for The total number of discrete points in the direction; These are the coordinates of the surface contact point; The radius of the grinding tool; For discrete points Normal vector at the point; The polar angle of the spiral trajectory point.

[0055] Furthermore, in step 5, in the post-processing model, the A-axis oscillates. The formulas for calculating the displacement and runout of the X and Z linear axes after the degree are as follows:

[0056] when hour:

[0057] ;

[0058] when hour:

[0059] ;

[0060] Displacement compensation amount and The calculation formula is:

[0061] , ;

[0062] In the formula: The lateral swing arm length of the L-shaped swing arm on swing axis A; This refers to the length of the vertical swing arm; The spindle axial projection distance from the tool holder mounting end face to the center of the tool profile; The radius of the tool hub; The radius of the tool profile; For swing axis A The displacement runout of the grinding point on the X-axis after grinding; For swing axis A The displacement runout of the grinding point on the Z-axis after grinding; for 0 o'clock value; for 0 o'clock value;

[0063] The complete motion coordinates in the machine tool coordinate system are:

[0064]

[0065] In the formula: and These are the transformed tool position coordinate components; This is the initial feed angle; , , and The final X-axis, Y-axis, Z-axis, and C-axis coordinates of the vertical oscillating machine tool; It is the remainder function;

[0066] The grinding feed rate is calculated using the following C-axis variable feed linear interpolation strategy. :

[0067]

[0068] In the formula: The rotational speed at the center of axis C; Let C be the rotational speed of the outer periphery of the rotating shaft; The radius of the aspherical surface corresponding to the grinding point; The radius of the outer circle of the aspherical aperture.

[0069] Compared with the prior art, the present invention has the following beneficial technical effects:

[0070] 1. High modeling accuracy and simple process: It abandons the cumbersome process of traditional CAD / CAM multi-software transfer, and directly generates discrete coordinates of aspherical space through numerical calculation. It eliminates Taylor expansion and coordinate transformation errors in off-axis aspherical modeling, and has high modeling accuracy. It can be arbitrarily adapted to optical surfaces with different grinding diameters, greatly simplifying the process preparation process.

[0071] 2. Synergistic Improvement of Grinding Efficiency and Surface Quality: The designed dual-mode adaptive helical machining trajectory with equal arc step size at the periphery and equal angle step size at the center ensures the uniformity of trajectory point distribution across the entire diameter. Combined with a C-axis variable feed linear interpolation strategy, it solves the problem of surface roughness deterioration caused by excessively low linear velocity in the central region of ordinary helical grinding. Grinding efficiency is increased to 8 times that of traditional grid grinding and 1.7 times that of ordinary helical grinding. The surface roughness Ra after fine grinding is significantly improved. 0.2μm;

[0072] 3. High accuracy of multi-axis linkage coordinate mapping: A post-processing model adapted to vertical sway type machine tool was constructed, which accurately compensated for the displacement sway of X and Z linear axes caused by the sway of A sway axis, and realized accurate mapping from optical design coordinates to machine tool motion coordinates, ensuring the machining accuracy of 4+1 axis linkage grinding.

[0073] 4. Highly practical and easy to promote: This method is application-oriented, with a simple process chain and low equipment dependence. All operations can be completed on existing high-precision CNC milling and grinding machines without significant machine tool modifications. Experimental verification shows that this method is suitable for grinding large-diameter optical coaxial / off-axis aspherical surfaces with a diameter of Φ600mm or more, achieving a high PV accuracy after fine grinding. With a diameter of 0.018mm, it meets the stringent requirements of subsequent polishing processes, providing a reliable technical path for the engineering manufacturing of meter-scale large-diameter optical complex curved surfaces. Attached Figure Description

[0074] Figure 1 The diagrams show the global optical coordinate system, off-axis mirror local coordinate system, and machine tool coordinate system established in step 1 of embodiment 1 of the present invention, as well as the off-axis aspherical surface extraction diagram. (a) is a schematic diagram of the global optical coordinate system, off-axis mirror local coordinate system, and machine tool coordinate system, and (b) is a schematic diagram of off-axis aspherical surface extraction.

[0075] Figure 2This is a schematic diagram of the discrete strategy for the dual-modal adaptive discrete spiral machining trajectory designed in step 3 of embodiment 1 of the present invention. (a) is an overall schematic diagram, and (b) is a partial enlarged view of (a).

[0076] Figure 3 This is a schematic diagram of the shaft system configuration of the vertical oscillating machine tool used in step 5 of embodiment 1 of the present invention;

[0077] Figure 4 This is a schematic diagram of the kinematic model of the A-axis of the vertical oscillating machine tool in step 5 of embodiment 1 of the present invention;

[0078] Figure 5 The curves showing the surface roughness as a function of grinding radius under the existing fixed feed strategy are shown.

[0079] Figure 6 The diagram shows the trajectory curve of the Φ860mm JGS1 convex coaxial aspherical surface in Embodiment 1 of the present invention. (a) is a schematic diagram of the discrete coordinates of the aspherical surface space, (b) is a schematic diagram of the dual-mode adaptive discrete spiral machining trajectory, (c) is a schematic diagram of the spiral trajectory points of the discrete surface, (d) is a schematic diagram of the normal vector at the spiral trajectory points of the discrete surface, (e) is a schematic diagram of the spatial coordinates of the tool position point, and (f) is a schematic diagram of the C-axis linkage machining trajectory coordinates.

[0080] Figure 7 The diagram shows the trajectory curve of the Φ630mm microcrystalline glass concave off-axis aspherical surface in Embodiment 2 of the present invention. (a) is a schematic diagram of the discrete coordinates of the aspherical surface space, (b) is a schematic diagram of the dual-mode adaptive discrete spiral machining trajectory, (c) is a schematic diagram of the discrete surface spiral trajectory points, (d) is a schematic diagram of the normal vector at the discrete surface spiral trajectory points, (e) is a schematic diagram of the tool position point space coordinates, and (f) is a schematic diagram of the C-axis linkage machining trajectory coordinates.

[0081] Figure 8 This is a schematic diagram of the detection results of the Φ860mm JGS1 convex coaxial aspherical surface in Embodiment 1 of the present invention. (a) is the machine tool detection result, and (b) is the coordinate measuring machine detection result.

[0082] Figure 9 This is a schematic diagram of the detection results of the Φ630mm microcrystalline glass concave off-axis aspherical surface in Embodiment 2 of the present invention. (a) is the machine tool detection result, and (b) is the coordinate measuring machine detection result. Detailed Implementation

[0083] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0084] Example 1

[0085] This embodiment presents a 4+1 axis helical grinding method for large-diameter optical complex curved surfaces, applicable to the grinding of large-diameter coaxial / off-axis aspherical optical surfaces with diameters of Φ600mm and above, including convex / concave aspherical surfaces made of JGS1 (optical glass) and microcrystalline glass. After grinding, the surface accuracy PV≤0.018mm, the surface roughness Ra≤0.2μm, and the grinding efficiency is 8 times that of traditional grid grinding and 1.7 times that of ordinary helical grinding.

[0086] Specifically, this embodiment describes a 4+1 axis helical grinding method for large-diameter optical complex curved surfaces, which mainly includes the following steps:

[0087] Step 1: Construction of Multi-Coordinate Systems and Mathematical Modeling of Off-Axis Aspherical Surfaces

[0088] See Figure 1 Establish a global optical coordinate system (O) XYZ), off-axis mirror local coordinate system (O' X'Y'Z') and machine tool coordinate system (M X m Y m Z m C) Construct a rotationally symmetric aspherical mathematical model based on the standard aspherical equations in the global optical coordinate system. Specifically, the expression of the rotationally symmetric aspherical mathematical model is as follows:

[0089] ;

[0090] In the formula: radial coordinates At the height of the arrow, , and These are the X-axis and Y-axis coordinates in the global optical coordinate system, respectively. For vertex curvature, , The vertex radius of curvature; It is the conic constant; These are higher-order coefficients for aspherical surfaces; The order of the higher-order terms.

[0091] Off-axis aspherical surfaces are defined by the standard aspherical surface based on the amount of off-axis. The coordinates of the off-axis mirror are derived from the geometric aperture of the mirror. First, coordinate translation is used to obtain the coordinates in the local coordinate system of the off-axis mirror. The translation formula is:

[0092] ;

[0093] In the formula: , and These are the intermediate coordinates after translation; Off-axis quantity; The Z-axis coordinate in the global optical coordinate system; The center sagitta of the off-axis mirror.

[0094] Then, the mathematical model of the off-axis aspherical surface in the local coordinate system of the off-axis mirror is obtained through the off-axis angle Givens rotation transformation. The coordinate transformation formula of the off-axis angle Givens rotation transformation is:

[0095] ;

[0096] ;

[0097] In the formula: , and These are the coordinates in the local coordinate system of the off-axis mirror; It is the off-axis angle; and Radial coordinates and radial coordinates The height of the arrow at the location; The upper limit of the radial coordinate; This represents the lower limit of the radial coordinate.

[0098] Step 2: Generation of Discrete Coordinates in Aspherical Space

[0099] Abandoning the traditional CAM software process flow, based on the off-axis aspherical mathematical model, it directly generates discrete coordinates of the aspherical space through numerical calculation, realizing the autonomous and controllable generation from optical equations to machining trajectories.

[0100] Step 3: Dual-modal adaptive discrete spiral machining trajectory planning

[0101] Based on Archimedes' plane spiral curve equation, see [link / reference] Figure 2 A dual-modal adaptive discrete spiral machining trajectory with equal arc step size on the periphery and equal angle step size on the center is designed to obtain the planar spiral point.

[0102] Specifically, the formula for calculating the discrete point helical radius of the dual-modal adaptive discrete helical machining trajectory is as follows:

[0103] ;

[0104] In the formula: Located at the polar angle discrete points of location The corresponding polar radius; Located at the polar angle discrete points of location The corresponding polar radius; To specify the helix pitch; For the first Global increment of discrete points in the layer. = ; For the rotation period, ; ;j ; This represents the total number of spiral rotations from the center to the edge. , The radius of the outer circle of the aspherical aperture; Let be the number of discrete points in each spiral trajectory. ; For discrete points Polar angle increment;

[0105] discrete points Polar angle increment satisfy:

[0106] ;

[0107] In the formula: Specify the angle step size; To specify the angle step size corresponding to the arc step size, ; Specify the arc step size;

[0108] The dual-modal adaptive discrete spiral machining trajectory is as follows:

[0109] ;

[0110] By mapping the planar spiral points to the discrete coordinates of the aspherical space generated in step 2 using bilinear interpolation, the discrete surface spiral trajectory points are obtained. The interpolation equation is:

[0111] ;

[0112] In the formula: For discrete points The arrow is high; For discrete points Distance-based weighting coefficients; For discrete points At the point of elevation, discrete point For discrete points The neighboring point.

[0113] Step 4: Tool position point calculation and coordinate system transformation

[0114] The finite difference method is used to solve for the normal vector at the discrete surface spiral trajectory point generated in step 3, and the spatial coordinates of the tool position point are calculated in combination with the grinding tool radius.

[0115] Specifically, when using the finite difference method to solve for the normal vector at the points of the discrete surface spiral trajectory, the partial derivatives are calculated using the central difference method for interior points to ensure calculation accuracy; for boundary points, since there are no symmetrical neighbors, the partial derivatives are calculated using the one-way difference method. The formula for calculating the partial derivatives when applying the central difference method to interior points is as follows:

[0116] ;

[0117] When applying one-way difference to boundary points, the formula for calculating partial derivatives is as follows:

[0118] Left boundary: Right boundary: Upper boundary: Lower boundary: .

[0119] Then through the pre-built winding Rotation matrix of axis Convert the tool position spatial coordinates into C-axis rotary axis linkage machining trajectory coordinates. , .

[0120] Tool position coordinates This is the distance by which the surface contact point is offset outward from the tool radius along the normal vector, i.e.:

[0121] ;

[0122] ;

[0123] In the formula: For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; for The total number of discrete points in the direction; for The total number of discrete points in the direction; These are the coordinates of the surface contact point; The radius of the grinding tool; For discrete points Normal vector at the point; The polar angle of the spiral trajectory point.

[0124] Step 5, 4+1 axis linkage grinding control

[0125] See Figure 3 and Figure 4 The existing vertical oscillating machine tool's axis system includes the X linear axis, Y linear axis, Z linear axis, C rotary axis, and A oscillating axis, i.e., 4+1 axes.

[0126] A post-processing model for an existing vertical oscillating machine tool is constructed. In the post-processing model of the vertical oscillating machine tool, the A-axis oscillates. The formulas for calculating the displacement and runout of the X and Z linear axes after the degree are as follows:

[0127] when hour:

[0128] ;

[0129] when hour:

[0130] ;

[0131] by Using 0° as the reference, calculate the oscillation of axis A. Displacement compensation amount after degree and :

[0132] , ;

[0133] In the formula: The lateral swing arm length of the L-shaped swing arm on swing axis A; This refers to the length of the vertical swing arm; The spindle axial projection distance from the tool holder mounting end face to the center of the tool profile; The radius of the tool hub, The radius of the tool profile; For swing axis A The displacement runout of the grinding point on the X-axis after grinding; For swing axis A The displacement runout of the grinding point on the Z-axis after grinding; for 0 o'clock value; for 0 o'clock value.

[0134] The post-processing model described above compensates for the displacement yaw of the X and Z linear axes caused by the A oscillating axis, and superimposes it with the C rotary axis linkage machining trajectory coordinates obtained in step 4 to obtain the complete motion coordinates in the machine tool coordinate system. The complete motion coordinates in the machine tool coordinate system are:

[0135]

[0136] In the formula: and These are the transformed tool position coordinate components; This is the initial feed angle; , , and The final X-axis, Y-axis, Z-axis, and C-axis coordinates of the vertical oscillating machine tool; It is the modulo function.

[0137] See Figure 5Existing fixed feed strategies tend to lead to uneven surface roughness distribution. To address this issue, the grinding feed trajectory is controlled according to complete motion coordinates. A pre-constructed linear interpolation strategy with low peripheral rotation speed and high central rotation speed on the C-axis is employed to adjust the grinding feed speed in real time, thereby optimizing the uniformity of surface roughness distribution and enabling 4+1 axis helical grinding of large-diameter optical complex curved surfaces.

[0138] The grinding feed rate is calculated using a C-axis rotary variable feed linear interpolation strategy. The formula is:

[0139]

[0140] In the formula: The rotational speed at the center of axis C; Let C be the rotational speed of the outer periphery of the rotating shaft; The radius of the non-spherical surface corresponding to the grinding point.

[0141] See Figure 6 This embodiment employs a 4+1 axis helical grinding method for large-diameter optical complex curved surfaces, using a Φ860mm JGS1 convex coaxial aspherical surface as the machining object for grinding:

[0142] In step 1, the vertex radius of curvature of the rotationally symmetric aspherical mathematical model 2297mm, conic constant 0, higher-order coefficients of aspherical surfaces 4e 11. 6.5e 18. 1.4e 23. Concavity / convexity parameter U 1 (convex surface).

[0143] In step 3, set the specified helical pitch. 0.3mm, the angle step corresponding to the specified arc step. 10°, specifying the arc step size 10mm.

[0144] In step 4, the radius of the selected grinding tool is... 50mm.

[0145] In step 5, an AGM1600 machine tool is used to compensate for the swing angle of the A-axis through its post-processing model. 50° displacement runout; C-axis variable feed speed 4.1~7.1 r / min, grinding depth decreasing in layers (0.15mm→0.05mm→0.03mm); copper-based hemispherical diamond grinding wheel (100mm diameter, D40 grit) is selected, spindle speed 3651 r / min.

[0146] After grinding, in-situ online inspection is performed: the Renishaw LP2 probe is integrated into the tail end of the A swing shaft, and surface data is collected using a grid-type inspection path.

[0147] See Figure 8 Error compensation and accuracy assessment: The detection data was corrected using a ball head radius detection error compensation model. The online detection surface accuracy PV was 0.015mm, and the surface roughness Ra was [not specified]. The thickness is 0.2μm, with a deviation of only 0.001mm from the three-coordinate measurement result (PV 0.014mm), which meets the polishing requirements.

[0148] In this embodiment, the fine grinding time per cut is about 4 hours, and the total time to remove 0.311mm of asphericity is 16 hours. The grinding efficiency is 8 times that of traditional grid grinding and 1.7 times that of ordinary spiral grinding.

[0149] Example 2

[0150] See Figure 7 The difference between this embodiment and Embodiment 1 is that: a Φ630mm microcrystalline glass concave off-axis aspherical surface is used as the processing object, with an off-axis distance of 350mm and a vertex radius of curvature. 4000mm, conic constant 1. Concavity / convexity parameter U 1 (concave surface), the swing angle of axis A is 45°, C-axis variable feed speed 5.1~7.1r / min; resin-based spherical cap diamond grinding wheel (diameter 200mm, grit size D76) is selected, spindle speed 2371r / min.

[0151] The other grinding parameters in this embodiment are the same as in Embodiment 1.

[0152] See Figure 9 Error compensation and accuracy assessment: After error compensation, the surface accuracy PV is 0.017mm and the surface roughness Ra is [missing information]. The thickness is 0.2μm, which deviates from the three-coordinate measurement result (PV 0.018mm) by 0.001mm, meeting the polishing requirements.

[0153] In this embodiment, the fine grinding time per cut is about 3 hours, and the total time to remove 0.065mm of asphericity is 12 hours, which significantly improves grinding efficiency.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for 4+1 axis helical grinding of large-diameter optical complex curved surfaces, characterized in that, Includes the following steps: Step 1: Construction of Multi-Coordinate Systems and Mathematical Modeling of Off-Axis Aspherical Surfaces Establish a global optical coordinate system, an off-axis mirror local coordinate system, and a machine tool coordinate system. Based on the standard aspherical equations in the global optical coordinate system, construct a rotationally symmetric aspherical mathematical model. Then, obtain the off-axis aspherical mathematical model in the local coordinate system through coordinate translation and Givens rotation transformation of the off-axis angle. Step 2: Generation of Discrete Coordinates in Aspherical Space Based on the mathematical model of off-axis aspherical surfaces, discrete coordinates of aspherical space are directly generated through numerical calculation. Step 3: Dual-modal adaptive spiral trajectory planning Based on the Archimedes plane spiral curve equation, a dual-modal adaptive discrete spiral machining trajectory with an outer equal arc step size and a central equal angle step size is designed to obtain the plane spiral points; further, the plane spiral points are mapped to the aspherical space discrete coordinates generated in step 2 through bilinear interpolation to obtain the discrete surface spiral trajectory points. Step 4: Tool position point calculation and coordinate system transformation The finite difference method is used to solve for the normal vector at the discrete surface spiral trajectory point generated in step 3. The tool position spatial coordinates are calculated in combination with the grinding tool radius. Then, the tool position spatial coordinates are converted into C-axis linkage machining trajectory coordinates through a pre-constructed rotation matrix. Step 5, 4+1 axis linkage grinding control A post-processing model for a vertical oscillating machine tool is constructed. This model compensates for the displacement oscillation of the X and Z linear axes caused by the oscillation of the A oscillating axis. The model is then superimposed with the C rotary axis linkage machining trajectory coordinates obtained in step 4 to obtain the complete motion coordinates in the machine tool coordinate system. The grinding feed trajectory is controlled according to the complete motion coordinates. A pre-constructed C rotary axis variable feed linear interpolation strategy with low speed on the periphery and high speed on the center is adopted to adjust the grinding feed speed in real time, thereby realizing 4+1 axis helical grinding of large-diameter optical complex curved surfaces.

2. The method for 4+1 axis helical grinding of large-diameter optical complex curved surfaces according to claim 1, characterized in that, In step 1, the expression for the rotationally symmetric aspherical mathematical model is: ； In the formula: radial coordinates At the height of the arrow, , and These are the X-axis and Y-axis coordinates in the global optical coordinate system, respectively. For vertex curvature, , The vertex radius of curvature; It is the conic constant; These are higher-order coefficients for aspherical surfaces; The order of the higher-order terms; The translation formula used for coordinate translation is: ； In the formula: , and These are the intermediate coordinates after translation; Off-axis quantity; The Z-axis coordinate in the global optical coordinate system; The center sagitta of the off-axis mirror; When performing the Givens rotation transformation around the off-axis mirror, the coordinate transformation formula used for rotation about the X' axis in the local coordinate system of the off-axis mirror is as follows: ； ； In the formula: , and These are the coordinates in the local coordinate system of the off-axis mirror; It is the off-axis angle; and Radial coordinates and radial coordinates The height of the arrow at the location; The upper limit of the radial coordinate; This represents the lower limit of the radial coordinate.

3. The method for 4+1 axis helical grinding of large-diameter optical complex curved surfaces according to claim 2, characterized in that, In step 3, the formula for calculating the discrete point helical radius of the dual-modal adaptive discrete helical machining trajectory is as follows: ； In the formula: Located at the polar angle discrete points of location The corresponding polar radius; Located at the polar angle discrete points of location The corresponding polar radius; To specify the helix pitch; For the first Global increment of discrete points in the layer. = ; For the rotation period, ; ;j ; This represents the total number of spiral rotations from the center to the edge. , The outer radius of the aspherical aperture; Let be the number of discrete points in each spiral trajectory. ; For discrete points Polar angle increment; discrete points Polar angle increment satisfy: ； In the formula: Specify the angle step size; To specify the angle step size corresponding to the arc step size, ; Specify the arc step size; The dual-modal adaptive discrete spiral machining trajectory is as follows: ； By mapping the planar spiral points to the discrete coordinates of the aspherical space generated in step 2 using bilinear interpolation, the discrete surface spiral trajectory points are obtained. The interpolation equation is: ； In the formula: For discrete points The arrow is high; For discrete points Distance-based weighting coefficients; For discrete points At the point of elevation, discrete point For discrete points The neighboring point.

4. The method for 4+1 axis helical grinding of large-diameter optical complex curved surfaces according to claim 1, characterized in that, In step 4, when using the finite difference method to solve for the normal vector at the point of the discrete surface spiral trajectory, the central difference is applied to the internal points and the one-way difference is applied to the boundary points. When applying central difference to interior points, the formula for calculating partial derivatives is as follows: ； When applying one-way difference to boundary points, the formula for calculating partial derivatives is as follows: Left boundary: Right boundary: Upper boundary: Lower boundary: ; Tool position spatial coordinates The calculation formula is: ； ； By pre-constructing the machine tool coordinate system Rotation matrix of axis Convert the tool position spatial coordinates into C-axis rotary axis linkage machining trajectory coordinates. , ; In the formula: For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points Distorted Derivative; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; For discrete points The arrow is high; In order to be in The distance between two adjacent discrete points in the direction; For discrete points The arrow is high; For discrete points The arrow is high; for The total number of discrete points in the direction; for The total number of discrete points in the direction; These are the coordinates of the surface contact point; The radius of the grinding tool; For discrete points Normal vector at the point; The polar angle of the spiral trajectory point.

5. A method for 4+1 axis helical grinding of large-diameter optical complex curved surfaces according to claim 1 or 4, characterized in that, In step 5, in the post-processing model, the A-axis oscillates. The formulas for calculating the displacement and runout of the X and Z linear axes after the degree are as follows: when hour: ； when hour: ； Displacement compensation amount and The calculation formula is: ， ； In the formula: The lateral swing arm length of the L-shaped swing arm on swing axis A; This refers to the length of the vertical swing arm; The spindle axial projection distance from the tool holder mounting end face to the center of the tool profile; The radius of the tool hub; The radius of the tool profile; For swing axis A The displacement runout of the grinding point on the X-axis after grinding; For swing axis A The displacement runout of the grinding point on the Z-axis after grinding; for 0 o'clock value; for 0 o'clock value; The complete motion coordinates in the machine tool coordinate system are: ； In the formula: and These are the transformed tool position coordinate components; This is the initial feed angle; , , and The final X-axis, Y-axis, Z-axis, and C-axis coordinates of the vertical oscillating machine tool; It is the remainder function; The grinding feed rate is calculated using the following C-axis variable feed linear interpolation strategy. : ； In the formula: The rotational speed at the center of axis C; Let C be the rotational speed of the outer periphery of the rotating shaft; The radius of the aspherical surface corresponding to the grinding point; The radius of the outer circle of the aspherical aperture.

Images