Compensation processing method and system for nonlinear time control grinding of complex curved surface

Abstract

This invention discloses a nonlinear time-controlled grinding compensation method for complex curved surfaces, applied to a nonlinear time-controlled grinding compensation system for complex curved surfaces. The method includes the following steps: S1, measuring the initial surface shape error D(x, y) of the workpiece; S2, establishing a contact force mathematical model and obtaining the nonlinear compensation factor δ(x, y); S3, performing nonlinear compensation on the initial surface shape error D(x, y) of the workpiece, resulting in a compensated surface shape error D'(x, y) = D(x, y) / δ(x, y); S4, calculating the dwell time and material removal amount based on the compensated surface shape error D'(x, y), and performing time-controlled grinding on the initial surface of the workpiece. A nonlinear time-controlled grinding compensation system for complex curved surfaces is also disclosed. This nonlinear time-controlled grinding compensation method and system for complex curved surfaces has advantages such as applicability to complex curved surface machining and significant improvement in convergence rate and machining accuracy.

Description

Technical Field

[0001] This invention relates to the field of optical component processing technology, specifically to a method and system for nonlinear time-controlled grinding compensation of complex curved surfaces. Background Technology

[0002] The growing demand for complex curved optical components is increasingly at odds with the insufficient micrometer-level machining precision of current methods. In the traditional grinding-laden grinding-polishing process chain, precision grinding can only achieve machining precision at the tens of micrometer level, which cannot meet the precision requirements of the polishing process. Laden grinding can serve as a transitional process before polishing, but it suffers from low machining precision and long processing cycles due to poor contact and edge effects. Ultra-precision grinding (UPG) can achieve micrometer-level surface accuracy, but it introduces deep grinding marks that are difficult to remove through polishing, still requiring a laden grinding process, which further reduces machining precision.

[0003] In the manufacturing of complex curved optical components, especially large-aperture components, advanced processes such as magnetorheological polishing (MRF) and ion beam shaping (IBF) can efficiently achieve nanometer-level precision machining. However, problems such as insufficient grinding accuracy and low deterministic shaping performance significantly prolong the development cycle of complex curved optical components. Studies have shown that the time consumed in grinding and lapping complex curved surfaces to micrometer-level precision accounts for approximately 80% of the total machining cycle, becoming a key constraint to achieving efficient manufacturing.

[0004] Traditional manufacturing of complex curved optical components typically follows a sequential process of grinding, lapping, and polishing. Grinding offers high material removal rates and is used to shape mirror blanks, achieving the basic geometric configuration of the optical component; however, its machining accuracy depends entirely on the motion accuracy of the machine tool. Lapping can homogenize grinding marks and remove grinding damage, but it suffers from low processing efficiency and significant edge effects. Often, repeated cycles of grinding and inspection are required to improve the surface accuracy to a level suitable for interferometric testing, preparing it for computer-controlled optical surface shaping (CCOS) polishing. CCOS polishing offers high material removal resolution and ultra-high machining accuracy, with the primary goal of reducing surface errors from the micrometer level to the nanometer level to meet the requirements of optical systems.

[0005] CCOS technology was first proposed by Itek in the United States. This technology uses a polishing tool with a diameter much smaller than the workpiece to extract a removal function, which is then convolved with the surface shape error to calculate the dwell time required to remove high-error areas. By controlling the dwell time of the polishing tool, precise error removal is achieved. As a time-controlled machining method, CCOS can achieve nanometer or even sub-nanometer precision without relying on machine tool trajectory accuracy.

[0006] Currently, small-diameter planar and spherical optical elements can achieve micron-level precision directly through ultra-precision grinding (UPG), and after smoothing, they can be directly subjected to interferometry and CCOS polishing. In contrast, complex curved optical elements, especially those with high steepness, still lack efficient processing methods to directly achieve micron-level precision. The main reason is that these elements have large local curvature and drastic steepness changes, making it difficult for both conventional and ultra-precision grinding to meet the precision requirements. Furthermore, the low determinism of grinding leads to slow precision improvement. The iterative grinding-inspection process required to achieve micron-level surface accuracy is time-consuming and labor-intensive, severely restricting the manufacturing efficiency of complex curved optical elements. Therefore, the challenge of efficient and low-cost manufacturing of complex curved optical elements has become one of the key bottlenecks restricting the rapid development and application of high-end optical equipment.

[0007] To address the bottlenecks in the micron-level precision manufacturing of complex curved optical components, scholars both domestically and internationally have conducted systematic research on material removal mechanisms, large-diameter complex curved surface manufacturing, and process optimization. Regarding the optimization of material removal mechanisms, existing technologies have proposed a single-point oblique-axis grinding error compensation method that considers wheel wear. By real-time monitoring of the grinding wheel's condition using an in-situ wear detection system and establishing a wear model using advanced image processing technology, the machining accuracy of aspherical glass molds for optical applications has been significantly improved. Existing technologies also comprehensively review the material removal mechanisms during the grinding process, pointing out that almost all grinding parameters, such as grinding force, surface accuracy, and surface integrity, affect material removal behavior, laying a theoretical foundation for establishing accurate mathematical models.

[0008] In the manufacturing of large-aperture complex curved surfaces, existing technologies have successfully developed a 4-m diameter SiC aspherical mirror. By optimizing the error surface segmentation strategy, a surface accuracy of 1 / 40λRMS was achieved, marking the first successful case of this size and material combination and verifying the effectiveness of multi-tool collaborative processing. Existing technologies also propose a large-aperture CCOS polishing tool equipped with a composite motion unit for the rapid manufacturing of Ø15 m off-axis parabolic components, significantly improving manufacturing efficiency. Furthermore, existing technologies propose a multi-tool parallel processing framework for large optical components, effectively shortening the manufacturing cycle through synchronous multi-tool operation.

[0009] In terms of process optimization, existing technologies have proposed a composite polishing method combining dual-rotor polishing and spin polishing to address two core edge effect problems in CCOS: nonlinear distribution of edge pressure and the inability to remove edges. A corresponding theoretical model has been established, effectively improving edge processing quality. Existing technologies have also investigated the influence of magnetorheological polishing trajectories on the mid-frequency error of optical surfaces. Experimental results show that a reasonable trajectory design can reduce the mid-frequency error by approximately 35%, providing important guidance for error control. For ultra-precision machining of weakly stiff planar mechanical parts, existing technologies have proposed time-controlled grinding (TCG) based on CCOS and flexible grinding technology, achieving high-precision machining. Nevertheless, most existing research focuses on process optimization for planar or low-steep curved surfaces, and research on the micron-level precision manufacturing of high-steep complex curved surfaces remains relatively lacking.

[0010] Time-controlled grinding (TCG), proposed by the National University of Defense Technology, combines the high removal efficiency of grinding with the deterministic shaping capability of CCOS, demonstrating excellent performance in the manufacture of precision components such as planes and cylinders. Existing technologies have used TCG to achieve in-situ inspection and sub-micron precision machining of ultra-precision hydrostatic guideways. This method has also been applied to ultra-precision air-static spindles, achieving a spindle machining accuracy better than 0.1 µm, exceeding the machining accuracy of traditional ultra-precision cylindrical grinding machines. However, current TCG methods, such as the TCG machining method, system, and medium for optical elements disclosed in Chinese patent application number 202111227785.2, rely on contact wheel pressure for material removal, specifically showing that the removal efficiency in low-steepness regions is significantly higher than in high-steepness regions. This deviation is mainly caused by the change in the component of the tool's gravity along the normal direction of the curved surface. As a result, the constant force output of the cylinder of the time-controlled grinding machine cannot effectively offset the difference in the gravity component, causing the actual contact pressure to deviate from the preset value. This makes it difficult to process complex curved surfaces with high steepness or off-axis. When processing large-diameter, high steepness or off-axis curved surfaces, the convergence rate is low and the processing accuracy is poor. Summary of the Invention

[0011] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a nonlinear time-controlled grinding compensation method and system for complex curved surfaces that can be applied to the machining of complex curved surfaces and can significantly improve the convergence rate and machining accuracy.

[0012] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for nonlinear time-controlled grinding compensation of complex curved surfaces is applied to a nonlinear time-controlled grinding compensation system for complex curved surfaces. The system includes a base, a mounting base, a tape winding module, a tape unwinding module, a contact wheel, an abrasive belt, a machining cylinder, and a balancing cylinder. The base is swayable, and the mounting base slides on it. The machining cylinder is positioned between the base and the mounting base. The tape winding module, tape unwinding module, and contact wheel are all mounted on the mounting base. The abrasive belt connects the tape winding module and the tape unwinding module. The contact wheel contacts the workpiece via the abrasive belt. The machining cylinder provides the contact force between the contact wheel and the workpiece. The balancing cylinder balances the weight of the mounting base. The method includes the following steps: S1. Measure the initial surface shape error D(x, y) of the workpiece. S2. Establish the mathematical model of contact force and obtain the nonlinear compensation factor δ(x,y), including the following sub-steps: S21. Establish a mathematical model of the planar contact force of the workpiece. F0 = F2 - (F1 - G); Establish a mathematical model of the surface contact force on the initial surface of the workpiece. F = F2-(F1- G×cosθ) F1 is the output force of the balancing cylinder, F2 is the output force of the machining cylinder, G is the total weight of the mounting base, and θ is the angle between the normal vector of the machining point and the vertical direction. S22. Based on the curvature distribution of the initial surface of the workpiece at different spatial positions, calculate the nonlinear compensation factor δ(x,y) at the corresponding positions. δ (x,y)= F / F0= [F2- (F1- G×cosθ)] / [F2- (F1- G)]; S3. Perform nonlinear compensation on the initial surface shape error D(x,y) of the workpiece. The surface shape error after compensation is D'(x,y) = D(x,y) / δ(x,y). S4. Based on the compensated surface error D'(x,y), calculate the dwell time and material removal amount, and perform time-controlled grinding on the initial surface of the workpiece.

[0013] As a further improvement to the above technical solution: In S21, F1 and F2 are both constant output forces. In S4, the balance cylinder uses the output force in S21 as the constant output force.

[0014] 25N ≤ F2 ≤ 200N.

[0015] The extension and retraction direction of the processing cylinder is the same as the movement direction of the mounting base relative to the base.

[0016] The center of the contact wheel is located in the extension and retraction direction of the machining cylinder.

[0017] The extension and retraction direction of the balancing cylinder is the same as that of the machining cylinder.

[0018] The contact wheel is located at the bottom of the mounting base, the tape winding module and the tape unwinding module are located on both sides of the mounting base, and the processing cylinder is located between the tape winding module and the tape unwinding module.

[0019] The base is provided with a first guide rail, the mounting seat is provided with a second guide rail, the mounting seat is slidably mounted on the first guide rail, the balancing cylinder is located between the base and the mounting seat, the contact wheel is slidably mounted on the second guide rail, and the processing cylinder is located between the mounting seat and the contact wheel.

[0020] A complex curved surface nonlinear controlled-time grinding compensation system is provided to realize the aforementioned complex curved surface nonlinear controlled-time grinding compensation method. It includes a base, a mounting base, a tape winding module, a tape unwinding module, a contact wheel, an abrasive belt, a processing cylinder, and a balancing cylinder. The base is swayable, the mounting base slides on the base, the processing cylinder is positioned between the base and the mounting base, the tape winding module, the tape unwinding module, and the contact wheel are all mounted on the mounting base, the abrasive belt connects the tape winding module and the tape unwinding module, the contact wheel contacts the workpiece through the abrasive belt, the processing cylinder provides the contact force between the contact wheel and the workpiece, and the balancing cylinder balances the weight of the mounting base.

[0021] As a further improvement to the above technical solution: The contact wheel is located at the bottom of the mounting base, the tape winding module and the tape unwinding module are located on both sides of the mounting base, and the processing cylinder is located between the tape winding module and the tape unwinding module; the extension and retraction direction of the processing cylinder is the same as the movement direction of the mounting base relative to the base, the center of the contact wheel is located in the extension and retraction direction of the processing cylinder, and the extension and retraction direction of the balancing cylinder is the same as that of the processing cylinder.

[0022] Compared with the prior art, the advantages of the present invention are as follows: The nonlinear time-controlled grinding compensation method for complex curved surfaces of the present invention provides an effective technical approach to overcome the constraint between accuracy and efficiency in the manufacturing of complex curved surfaces. It is applicable to the machining of complex curved surfaces and can significantly improve the convergence rate and machining accuracy.

[0023] This complex surface nonlinear time-controlled grinding compensation system is used to realize the complex surface nonlinear time-controlled grinding compensation method. It has all the advantages of the complex surface nonlinear time-controlled grinding compensation method, that is, it can be applied to the machining of complex surfaces (such as high steep off-axis ellipsoids) and can significantly improve the convergence rate and machining accuracy. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the complex curved surface nonlinear time-controlled grinding compensation machining system of the present invention.

[0025] Figure 2 The comparison shows the surface shape of a high-steep off-axis workpiece before and after machining: (a) the initial surface shape of the workpiece before machining, (b) the surface shape after machining without compensation, and (c) the surface shape after machining using a complex curved surface nonlinear time-controlled grinding compensation machining method.

[0026] Figure 3 It is a surface layout diagram of a high-steep off-axis aspherical workpiece.

[0027] Figure 4 This is an experiment on surface shape error correction of a steep off-axis ellipsoid without nonlinear compensation. (a) shows the dwell time distribution, (b) shows the simulation results, and (c) shows the actual processing results. Figure 5 The experiment shows the surface shape error correction of a high-steep off-axis ellipsoid using this method. (a) shows the nonlinear compensation result, (b) shows the dwell time distribution, (c) shows the processing simulation result, and (d) shows the actual processing result.

[0028] Figure 6 This is a distribution diagram of volumetric removal efficiency in time-controlled grinding.

[0029] Figure 7 This is a graph showing the relationship between the output force F2 and the logarithmic values ​​of the nonlinear compensation shape error, log(PV) and log(RMS), where 0N ≤ F2 ≤ 100N.

[0030] Figure 8 This is a graph showing the relationship between the output force F2 and the logarithmic values ​​of the nonlinear compensation shape error, log(PV) and log(RMS), where 25N ≤ F2 ≤ 200N.

[0031] The labels in the diagram represent: 1. Base; 2. Mounting base; 3. Tape winding module; 4. Tape unwinding module; 5. Contact wheel; 6. Sanding belt; 7. Machining cylinder; 8. First guide rail; 9. Second guide rail. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] In the description of this invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0034] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0035] In this invention, unless otherwise explicitly specified and limited, the terms "assembly," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0036] Example 1: One embodiment of the nonlinear time-controlled grinding compensation method for complex curved surfaces of the present invention is applied to, for example, nonlinear time-controlled grinding compensation method for complex curved surfaces. Figure 1 The complex curved surface nonlinear time-controlled grinding compensation system shown includes a base 1, a mounting base 2, a tape winding module 3, a tape unwinding module 4, a contact wheel 5, an abrasive belt 6, a processing cylinder 7, and a balancing cylinder. The base 1 is swayable, and the mounting base 2 slides on the base 1. The processing cylinder 7 is located between the base 1 and the mounting base 2. The tape winding module 3, the tape unwinding module 4, and the contact wheel 5 are all located on the mounting base 2. The abrasive belt 6 connects the tape winding module 3 and the tape unwinding module 4. The contact wheel 5 contacts the workpiece through the abrasive belt 6. The processing cylinder 7 provides the contact force of the contact wheel 5 on the workpiece, and the balancing cylinder balances the weight of the mounting base 2. The complex curved surface nonlinear time-controlled grinding compensation method includes the following steps: S1. Measure the initial surface shape error D(x, y) of the workpiece. S2. Establish the mathematical model of contact force and obtain the nonlinear compensation factor δ(x,y), including the following sub-steps: S21. Establish a mathematical model of the planar contact force of the workpiece. F0 = F2 - (F1 - G); Establish a mathematical model of the surface contact force on the initial surface of the workpiece. F = F2-(F1- G×cosθ) F1 is the output force of the balancing cylinder, F2 is the output force of the machining cylinder 7, G is the total weight of the mounting base 2, and θ is the angle between the normal vector of the machining point and the vertical direction. S22. Based on the curvature distribution of the initial surface of the workpiece at different spatial positions, calculate the nonlinear compensation factor δ(x,y) at the corresponding positions. δ(x,y) = F / F0= [F2- (F1- G×cosθ)] / [F2- (F1- G)]; S3. Perform nonlinear compensation on the initial surface shape error D(x,y) of the workpiece. The surface shape error after compensation is D'(x,y) = D(x,y) / δ(x,y). S4. Based on the compensated surface error D'(x,y), calculate the dwell time and material removal amount, and perform time-controlled grinding on the initial surface of the workpiece.

[0037] A steep off-axis aspherical workpiece (optical element) with a diameter of 100 mm was selected as the workpiece to be processed to verify the processing effect of the nonlinear time-controlled grinding compensation method for complex curved surfaces of the present invention. The workpiece to be processed is an off-axis ellipsoid, and its initial surface shape distribution is as follows. Figure 3 As shown in the figure. The off-axis distance of the workpiece is 279.4987 mm. First, the dwell time is calculated using the surface shape error without nonlinear compensation, and the initial surface of the workpiece is subjected to time-controlled grinding for shaping. Subsequently, the initial surface of the workpiece is subjected to time-controlled grinding using the nonlinear time-controlled grinding compensation method for complex curved surfaces. The material removal rate is set to 100% in both cases. The surface shapes obtained after machining are shown in the figures. Figure 2 (b) and Figure 2 As shown in (c), Figure 2(a) shows the initial surface shape of the workpiece before machining, with initial surface shape errors of PV (peak amplitude of wavefront error) 13.209 μm and RMS (average fluctuation intensity of wavefront error) 2.514 μm. The residual surface shape error after solving for the dwell time using the surface shape error without nonlinear compensation and performing time-controlled grinding on the initial surface of the workpiece is PV 10.611 μm (convergence rate 19.7%) and RMS 1.764 μm (convergence rate 29.8%). However, the residual surface shape error after performing time-controlled grinding on the initial surface of the workpiece using the nonlinear time-controlled grinding compensation method for complex surfaces is PV 3.768 μm (convergence rate 64.5%) and RMS 0.690 μm (convergence rate 60.9%). It can also be observed that... Figure 2 (b) The surface distribution is still the same as Figure 2 (a) They are quite similar, with the right-hand high point corresponding to... Figure 2 (b) The high points of the surface distribution (i.e., the positions with the maximum machining sway angle) indicate poor machining convergence when using uncompensated surface errors. In contrast, Figure 2 (c) has a relatively flat surface distribution, and the PV value convergence rate after processing reaches 64.5%, indicating that the nonlinear time-controlled grinding compensation method for complex curved surfaces has a significant effect on improving processing accuracy.

[0038] A steep off-axis ellipsoid with a diameter of 330 mm was selected for process verification to validate the machining effect of the nonlinear time-controlled grinding compensation method for complex curved surfaces of this invention. First, the dwell time was calculated using the surface shape error without nonlinear compensation, and the initial surface of the workpiece was then subjected to time-controlled grinding for shaping. The dwell time distribution, simulation results, and actual machining results of this process are shown below. Figure 4 As shown in (a), (b), and (c), the total dwell time was 660.19 minutes, with simulation residual errors of PV 8.466 μm and RMS 0.101 μm, while the actual machining residual errors were PV 20.717 μm and RMS 2.558 μm. Subsequently, the initial surface of the workpiece was subjected to time-controlled grinding using the nonlinear time-controlled grinding compensation method for complex curved surfaces. Figure 4 The nonlinear compensation result of (a) is as follows Figure 5 As shown in (a), the errors are PV 36.556 μm and RMS 4.119 μm. The residence time distribution, simulation results, and actual processing results of this process are as follows: Figure 5As shown in (b), (c), and (d), the total dwell time was 474.09 minutes, with simulated residual errors of PV 6.084 μm and RMS 0.323 μm, while actual machining residual errors were PV 8.413 μm and RMS 1.027 μm. Experimental verification on a 330 mm diameter, steeply off-axis ellipsoidal surface showed that the workpiece surface shape accuracy PV value was improved from 20.717 μm after grinding (dwell time calculation for surface shape error without nonlinear compensation and time-controlled grinding to reshape the initial surface of the workpiece) to 8.413 μm, achieving a level of accuracy comparable to ultra-precision grinding without severe wear marks. Power spectral density analysis showed a significant reduction in low-frequency errors, meeting the conditions for polishing, and the machining effect was significantly better than traditional grinding processes.

[0039] This nonlinear time-controlled grinding compensation method for complex curved surfaces provides an effective technical approach to overcome the constraint between accuracy and efficiency in the manufacturing of complex curved surfaces. It is applicable to the machining of complex curved surfaces and can significantly improve the convergence rate and machining accuracy.

[0040] The volume removal efficiency of each removal function was calculated, and the results are as follows: Figure 6 As shown, it is evident that the actual removal efficiency of the removal function shown in the red box in the central area is slightly higher than the volumetric efficiency of the removal function shown in the blue box in the edge area. During the edge removal function processing, the base 1 swing angle reached 26.29°, with an overall efficiency deviation of 18.61%. The main reason for this efficiency deviation is... Figure 1 The diagram illustrates the change in the working state of the machining cylinder 7. When the machining cylinder 7 is not perpendicular to the horizontal plane, although the output force of the machining cylinder 7 can be preset, the self-weight balance state of the mounting base 2 continuously changes. To address this problem, this invention models the contact force of time-controlled grinding under different working states (planar and curved surfaces) to explore a compensation method for the nonlinear change in removal efficiency. Nonlinear compensation is applied to the initial surface shape error D(x, y) to improve convergence rate and machining accuracy.

[0041] Furthermore, in this embodiment, in S21, F1 and F2 are both constant output forces, and in S4, the balance cylinder uses the output force in S21 as the constant output force.

[0042] Furthermore, in this embodiment, 25N ≤ F2 ≤ 200N.

[0043] In time-controlled grinding compensation machining, the output force F1 of the balancing cylinder is used to balance the tool's own weight G. Therefore, F1 is usually set to be no less than G (F1≥G) and remains constant after setting. The machining force can be adjusted by setting different output forces F2 of the machining cylinder 7; however, if the output force F2 is too small, the machining efficiency will be low, and if it is too large, it will cause serious subsurface damage. Therefore, selecting an appropriate output force is crucial to balancing the relationship between efficiency and accuracy.

[0044] Depend on Figure 7 It can be seen that when the output force F2 is in the range of 0 N ≤ F2 ≤ 25 N, the surface shape error PV and RMS values ​​after nonlinear compensation fluctuate greatly, making error correction impossible. If a processing force within this range is selected in actual machining, it will be difficult to improve the surface shape accuracy.

[0045] like Figure 8 As shown, when F2 > 25 N, the surface shape error after nonlinear compensation gradually decreases from 65 μm to near the level before compensation. Considering that excessive machining force will cause severe subsurface damage to the workpiece surface, while insufficient force will lead to excessively long machining time, this invention selects 25 N ≤ F2 ≤ 200 N as the machining force. More preferably, F2 = 31.4 N is selected as the machining force, corresponding to a machining cylinder P2 setting of 0.10 MPa.

[0046] Furthermore, in this embodiment, the extension and retraction direction of the processing cylinder 7 is the same as the movement direction of the mounting base 2 relative to the base 1.

[0047] Furthermore, in this embodiment, the center of the contact wheel 5 is located in the extension and retraction direction of the machining cylinder 7, which is beneficial to improving machining stability.

[0048] Furthermore, in this embodiment, the extension and retraction direction of the balancing cylinder is the same as that of the machining cylinder 7.

[0049] Furthermore, in this embodiment, the contact wheel 5 is located at the bottom of the mounting base 2, the winding module 3 and the unwinding module 4 are located on both sides of the mounting base 2, and the processing cylinder 7 is located between the winding module 3 and the unwinding module 4. The winding module 3 includes a winding wheel, and the unwinding module 4 includes an unwinding wheel. The winding wheel and the unwinding wheel are respectively arranged on both sides of the mounting base 2, and the abrasive belt 6 connects the winding wheel and the unwinding wheel. The winding wheel and the unwinding wheel wind and unwind the abrasive belt 6, thereby realizing the grinding of the working surface.

[0050] Furthermore, in this embodiment, a first guide rail 8 is provided on the base 1, a second guide rail 9 is provided on the mounting base 2, the mounting base 2 is slidably mounted on the first guide rail 8, a balancing cylinder is disposed between the base 1 and the mounting base 2, a contact wheel 5 is slidably mounted on the second guide rail 9, and a processing cylinder 7 is disposed between the mounting base 2 and the contact wheel 5. Preferably, the first guide rail 8, the second guide rail 9, the balancing cylinder, and the processing cylinder 7 are all arranged in parallel.

[0051] Example 2: Figure 1 This invention illustrates an embodiment of the complex curved surface nonlinear time-controlled grinding compensation system. This system is used to implement the complex curved surface nonlinear time-controlled grinding compensation method of Embodiment 1. It includes a base 1, a mounting base 2, a tape winding module 3, a tape unwinding module 4, a contact wheel 5, an abrasive belt 6, a processing cylinder 7, and a balancing cylinder. The base 1 is swayable, and the mounting base 2 is slidably mounted on it. The processing cylinder 7 is positioned between the base 1 and the mounting base 2. The tape winding module 3, the tape unwinding module 4, and the contact wheel 5 are all mounted on the mounting base 2. The abrasive belt 6 connects the tape winding module 3 and the tape unwinding module 4. The contact wheel 5 contacts the workpiece through the abrasive belt 6. The processing cylinder 7 provides the contact force of the contact wheel 5 on the workpiece, and the balancing cylinder balances the weight of the mounting base 2.

[0052] This complex surface nonlinear time-controlled grinding compensation system is used to implement the complex surface nonlinear time-controlled grinding compensation method of Embodiment 1. It has all the advantages of the complex surface nonlinear time-controlled grinding compensation method, namely, it can be applied to the machining of complex surfaces (such as high-steep off-axis ellipsoids) and can significantly improve the convergence rate and machining accuracy.

[0053] Furthermore, in this embodiment, the contact wheel 5 is located at the bottom of the mounting base 2, the tape winding module 3 and the tape unwinding module 4 are located on both sides of the mounting base 2 respectively, and the processing cylinder 7 is located between the tape winding module 3 and the tape unwinding module 4; the extension and retraction direction of the processing cylinder 7 is the same as the movement direction of the mounting base 2 relative to the base 1, the center of the contact wheel 5 is located in the extension and retraction direction of the processing cylinder 7, and the extension and retraction direction of the balance cylinder is the same as that of the processing cylinder 7.

[0054] The center of the contact wheel 5 is located in the extension and retraction direction of the machining cylinder 7, which helps to improve machining stability. The winding module 3 includes a winding wheel, and the unwinding module 4 includes an unwinding wheel. The winding wheel and the unwinding wheel are respectively set on both sides of the mounting base 2, and the abrasive belt 6 connects the winding wheel and the unwinding wheel. The winding wheel and the unwinding wheel wind and unwind the abrasive belt 6, thereby realizing the grinding of the working surface.

[0055] Furthermore, in this embodiment, a first guide rail 8 is provided on the base 1, a second guide rail 9 is provided on the mounting base 2, the mounting base 2 is slidably mounted on the first guide rail 8, a balancing cylinder is disposed between the base 1 and the mounting base 2, a contact wheel 5 is slidably mounted on the second guide rail 9, and a processing cylinder 7 is disposed between the mounting base 2 and the contact wheel 5. Preferably, the first guide rail 8, the second guide rail 9, the balancing cylinder, and the processing cylinder 7 are all arranged in parallel.

[0056] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for nonlinear time-controlled grinding compensation machining of complex curved surfaces, characterized in that: A nonlinear time-controlled grinding compensation machining system for complex curved surfaces is applied. The system includes a base (1), a mounting base (2), a tape winding module (3), a tape unwinding module (4), a contact wheel (5), an abrasive belt (6), a machining cylinder (7), and a balancing cylinder. The base (1) is swayable, the mounting base (2) is slidably mounted on the base (1), the machining cylinder (7) is located between the base (1) and the mounting base (2), the tape winding module (3), the tape unwinding module (4), and the contact wheel (5) are all mounted on the mounting base (2), the abrasive belt (6) connects the tape winding module (3) and the tape unwinding module (4), the contact wheel (5) contacts the workpiece through the abrasive belt (6), the machining cylinder (7) provides the contact force of the contact wheel (5) on the workpiece, and the balancing cylinder balances the weight of the mounting base (2). The nonlinear time-controlled grinding compensation machining method for complex curved surfaces includes the following steps: S1. Measure the initial surface shape error D(x,y) of the workpiece. S2. Establish the mathematical model of contact force and obtain the nonlinear compensation factor δ(x,y), including the following sub-steps: S21. Establish a mathematical model of the planar contact force of the workpiece. F0 = F2 - (F1 - G); Establish a mathematical model of the surface contact force on the initial surface of the workpiece. F = F2 - (F1 - G×cosθ); F1 is the output force of the balancing cylinder, F2 is the output force of the machining cylinder (7), G is the total weight of the mounting base (2), and θ is the angle between the normal vector of the machining point and the vertical direction. S22. Based on the curvature distribution of the initial surface of the workpiece at different spatial positions, calculate the nonlinear compensation factor δ(x,y) at the corresponding positions. δ (x,y)= F / F0 = [F2 - (F1 - G×cosθ)] / [F2 - (F1 - G)] ; S3. Perform nonlinear compensation on the initial surface shape error D(x,y) of the workpiece. The surface shape error after compensation is D'(x,y) = D(x,y) / δ(x,y). S4. Based on the compensated surface error D'(x,y), calculate the dwell time and material removal amount, and perform time-controlled grinding on the initial surface of the workpiece.

2. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to claim 1, characterized in that: In S21, F1 and F2 are both constant output forces. In S4, the balance cylinder uses the output force in S21 as the constant output force.

3. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to claim 2, characterized in that: 25N ≤ F2 ≤ 200N.

4. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to claim 1, characterized in that: The extension and retraction direction of the processing cylinder (7) is the same as the movement direction of the mounting base (2) relative to the base (1).

5. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to claim 4, characterized in that: The center of the contact wheel (5) is located in the extension and retraction direction of the machining cylinder (7).

6. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to claim 1, characterized in that: The extension and retraction direction of the balancing cylinder is the same as that of the machining cylinder (7).

7. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to any one of claims 1 to 6, characterized in that: The contact wheel (5) is located at the bottom of the mounting base (2), the tape winding module (3) and the tape unwinding module (4) are located on both sides of the mounting base (2), and the processing cylinder (7) is located between the tape winding module (3) and the tape unwinding module (4).

8. The nonlinear time-controlled grinding compensation method for complex curved surfaces according to any one of claims 1 to 6, characterized in that: The base (1) is provided with a first guide rail (8), the mounting seat (2) is provided with a second guide rail (9), the mounting seat (2) is slidably mounted on the first guide rail (8), the balancing cylinder is located between the base (1) and the mounting seat (2), the contact wheel (5) is slidably mounted on the second guide rail (9), and the processing cylinder (7) is located between the mounting seat (2) and the contact wheel (5).

9. A nonlinear time-controlled grinding compensation system for complex curved surfaces, characterized in that: The method for nonlinear controlled-time grinding compensation machining of complex curved surfaces according to any one of claims 1 to 8 includes a base (1), a mounting base (2), a tape winding module (3), a tape unwinding module (4), a contact wheel (5), an abrasive belt (6), a machining cylinder (7), and a balancing cylinder. The base (1) is swayable, the mounting base (2) is slidably mounted on the base (1), the machining cylinder (7) is located between the base (1) and the mounting base (2), the tape winding module (3), the tape unwinding module (4), and the contact wheel (5) are all mounted on the mounting base (2), the abrasive belt (6) connects the tape winding module (3) and the tape unwinding module (4), the contact wheel (5) contacts the workpiece through the abrasive belt (6), the machining cylinder (7) provides the contact force of the contact wheel (5) on the workpiece, and the balancing cylinder balances the weight of the mounting base (2).

10. The complex curved surface nonlinear time-controlled grinding compensation system according to claim 9, characterized in that: The contact wheel (5) is located at the bottom of the mounting base (2), the tape winding module (3) and the tape unwinding module (4) are located on both sides of the mounting base (2), and the processing cylinder (7) is located between the tape winding module (3) and the tape unwinding module (4); the extension and retraction direction of the processing cylinder (7) is the same as the movement direction of the mounting base (2) relative to the base (1), the center of the contact wheel (5) is located in the extension and retraction direction of the processing cylinder (7), and the extension and retraction direction of the balancing cylinder is the same as that of the processing cylinder (7).

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