A method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel with high efficiency and low damage using a hemispherical resonator

Abstract

The present invention discloses a method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator, which relates to the technical field of ultra-precision machining of hemispherical resonators. The method aims to solve the problem that existing methods are difficult to optimize the process parameters while taking into account both the machining efficiency and machining quality of the hemispherical resonator under the premise of controlling the sub-surface damage of the hemispherical resonator. The present invention adopts a central composite experimental design method to establish a response surface model of the sub-surface damage depth, and with high efficiency and low sub-surface damage depth as constraints, determines the process parameters and their ranges that affect the surface damage of the workpiece, divides the machining process into a high-efficiency grinding stage and a low-damage grinding stage, establishes a damage suppression model to control the remaining theoretical sub-surface damage depth in the low-damage grinding stage to be less than the damage depth under the current grinding process parameters, and formulates a high-efficiency and low-damage machining process path. The method of the present invention improves the machining efficiency and machining quality of the hemispherical resonator.

Description

Technical Field

[0001] The present invention relates to the technical field of ultra-precision machining of hemispherical resonators, and in particular to a method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of hemispherical resonators. Background Art

[0002] With the rapid development of ultraprecision machining technology, core components in cutting-edge defense equipment such as rockets, satellites, ships, and intercontinental missiles are experiencing increasingly complex structures, miniaturization, and demanding machining requirements, placing stringent demands on their reliability and quality. Hemispherical resonators are a typical example of hemispherical resonators. They are made of fused quartz and subjected to ultraprecision grinding to ensure dimensional accuracy and geometric tolerances. Because fused quartz is typically hard and brittle, subsurface damage (SSD), such as pits and cracks, is unavoidable during the grinding process. The depth of the damaged layer not only affects the efficiency of subsequent magnetorheological polishing but also compromises the machining quality and reduces part performance. The current bottleneck in machining these components is how to balance machining efficiency and quality while controlling SSD. Furthermore, optimizing grinding process parameters to improve machining efficiency, minimize damage, and achieve high-quality grinding, while also considering the diamond grit size of small-diameter diamond ball-end grinding wheels (micrometer-scale, less than 10 μm), remains a key challenge. Summary of the Invention

[0003] The technical problems to be solved by the present invention are:

[0004] Existing methods for ultra-precision grinding of hemispherical resonators make it difficult to optimize process parameters while taking into account both the processing efficiency and quality of the resonator under the premise of controlling the sub-surface damage of the hemispherical resonator.

[0005] The present invention is to solve the above technical problems using the following technical solutions:

[0006] The present invention provides a method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding using a hemispherical resonator, comprising the following steps:

[0007] S1. Using the diamond abrasive grain size of the ball-end grinding wheel as the variable, a single-factor experiment was conducted on the workpiece.

[0008] S2. Measure the subsurface damage depth of the workpiece under different diamond abrasive grain sizes. Taking the minimum subsurface damage depth of the workpiece as the constraint and taking high-efficiency processing into consideration, determine the optimal grinding wheel abrasive grain size for machining hemispherical resonators.

[0009] S3. Based on the determined optimal grinding wheel abrasive grain size, a central composite experimental design method was used. The process parameters to be optimized were used as central composite design factors, and the subsurface damage depth was used as the response indicator to design a central composite experimental plan. A central composite experiment was conducted to measure the subsurface damage depth of the workpiece under each set of process parameters, and a response surface model of the subsurface damage depth was established.

[0010] S4. Based on the established response surface model of subsurface damage depth, the process parameters and their ranges that affect the workpiece surface damage are determined with high efficiency and low subsurface damage depth as constraints;

[0011] S5, dividing the machining process into a high-efficiency grinding stage and a low-damage grinding stage, measuring the initial subsurface damage of the workpiece blank, determining the process parameters of the high-efficiency grinding stage based on the process parameters and their ranges affecting the workpiece surface damage obtained in S4, and determining the number of grinding times under each process parameter based on the initial damage measurement results of the workpiece blank;

[0012] Based on the process parameters and their ranges that affect the workpiece surface damage obtained by S4, the process parameters of the low-damage grinding stage are determined, and grinding experiments are carried out to measure the sub-surface damage depth of the workpiece under different process parameters. A damage suppression model is established based on the superposition effect of damage to control the remaining theoretical sub-surface damage depth in the low-damage grinding stage to be less than or equal to the damage depth under the current grinding process parameters, so as to determine the number of grinding times under various process parameters, and finally obtain the small-diameter ball head grinding wheel grinding process path for high-efficiency and low-damage grinding with a hemispherical resonator.

[0013] Furthermore, in S2, it is determined that the optimal grinding wheel grain size for machining the hemispherical resonator is 5 to 7 μm.

[0014] Furthermore, the process parameters to be optimized in S3 include: grinding speed v s , grinding depth a p , feed speed f.

[0015] Furthermore, S3 includes the following processes:

[0016] S31, determine the grinding speed v s , grinding depth a p , the range of each process parameter of feed speed f, based on the determined optimal grinding wheel abrasive size, the central composite experimental design (CCD) method is adopted, the process parameters to be optimized are used as central composite design factors, and the subsurface damage depth is used as the response index to design the central composite experimental plan and carry out central composite experiments;

[0017] S32, measuring the subsurface damage depth under each set of process parameters in the experimental plan;

[0018] S33. The measured subsurface damage depth data are regressed using the least squares method to establish a response surface of the subsurface damage depth in the form of:

[0019]

[0020] Where y represents the subsurface damage depth, x i , x j represents the independent variable, β i Representation factor x i The corresponding first-order effect, β ij Represents different factors x i and x j The interaction between β ii Representation factor x i The quadratic term influence is taken into account, k represents the number of factors; the least squares algorithm is used to obtain the coefficients of the second-order response surface model.

[0021] Furthermore, the process parameters and their ranges that affect the surface damage of the workpiece are determined to be: feed speed: 30μm / s~40μm / s, grinding speed: 14m / s, and a processing method with gradually decreasing grinding depth is adopted in the low-damage grinding stage.

[0022] Furthermore, the damage suppression model described in S5 is:

[0023]

[0024] Where, SSD(a pi ,v si ,f i ,d gi ) is the subsurface damage depth corresponding to the current grinding process parameters, SSD init is the initial subsurface damage depth of the workpiece, a pi is the grinding depth corresponding to the current process.

[0025] Furthermore, the process path for the efficient grinding stage is formulated in S5 as follows:

[0026] Stage I: grinding wheel speed 71000r / min, workpiece speed 30r / min, grinding depth 5μm, feed speed 40μm / s, grinding until full surface grinding is completed;

[0027] Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 40 μm / s, 6 grinding passes;

[0028] Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 30 μm / s, grinding 2 times;

[0029] The process path for the low-damage grinding stage is formulated as follows:

[0030] Stage I: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 2 μm, feed speed 30 μm / s, grinding 2 times;

[0031] Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 1 μm, feed speed 30 μm / s, grinding 2 times;

[0032] Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.5 μm, feed speed 30 μm / s, 1 grinding pass;

[0033] Stage IV: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.1 μm, feed speed 30 μm / s, 1 grinding pass;

[0034] Stage V: grinding wheel speed 71000 r / min, workpiece speed 30 r / min, grinding depth 0 μm, feed speed 30 μm / s, grinding 1 time.

[0035] Furthermore, the method for measuring subsurface damage of a workpiece includes the following steps:

[0036] Step 1: Using the selected polishing process parameters, magnetorheological single-point polishing is performed on the sidewall surface of the component to form polishing spots;

[0037] Step 2: Cleaning and etching the polished workpiece;

[0038] Step 3: measuring the three-dimensional profile of the polishing spot, and intercepting its two-dimensional profile to obtain the cross-sectional profile of the polishing spot;

[0039] Step 4: Measure the horizontal distance D between the crack vanishing point in the polishing area and the polishing boundary line, and determine the position of the corresponding crack vanishing point on the cross-sectional profile of the polishing spot according to the polishing boundary line;

[0040] Step 5: Using the contour data of the grinding area, the contour of the removed material is fitted and reconstructed based on the cross-sectional contour of the polishing spot to obtain the fitted contour curve of the removed material. The shortest distance from the crack vanishing point on the cross-sectional contour of the polishing spot to the fitted contour curve of the removed material is calculated to obtain the sub-surface damage depth of the workpiece.

[0041] Furthermore, the polishing process parameters in step 1 are: polishing head speed 7000 r / min, polishing gap 80 μm, and polishing time 15 to 20 min.

[0042] Furthermore, the fitting contour curve of the removed material in step 5 is:

[0043]

[0044] Among them, x i and y i is the coordinate of point i on the fitting contour of the removed material, g(x,y) is the curve equation of the fitting contour of the removed material, R is the radius of the fitting contour, x o and y o is the center of the fitting circle;

[0045] The relationship between the crack vanishing point and the polishing junction point on the cross-sectional contour line of the polishing spot is:

[0046] x cv =x pi +D

[0047] Among them, x cv and x pi are the horizontal coordinates of the crack vanishing point and the polishing junction point, respectively;

[0048] The shortest distance between the crack vanishing point on the polishing spot cross-sectional profile and the fitted contour curve of the removed material is calculated as:

[0049]

[0050] Among them, x c and y c is the intersection of the line connecting the crack vanishing point and the center of the fitting circle and the fitting circle, that is:

[0051]

[0052] Compared with the prior art, the beneficial effects of the present invention are: with high efficiency and low subsurface damage depth as constraints,

[0053] The present invention discloses a method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding using a hemispherical resonator. The method uses a response surface methodology to determine key process parameters and their ranges that affect machining efficiency and workpiece surface damage depth. A damage suppression model is established based on the superposition effect of damage. The damage suppression model is used to control the remaining theoretical sub-surface damage depth in the low-damage grinding stage to be smaller than the damage depth under the current grinding process parameters, thereby formulating a high-efficiency and low-damage ultra-precision grinding process route.

[0054] By adopting the high-efficiency and low-damage ultra-precision grinding process route of the hemispherical resonator formulated by the method of the present invention, the grinding processing time can be reduced by up to 33.3%, thereby greatly improving the processing efficiency of the hemispherical resonator.

[0055] By adopting the method of the present invention to perform ultra-precision machining on a hemispherical resonator, the subsurface damage depth of the outer spherical surface can be reduced by up to 92%, which helps to reduce the workload of subsequent polishing and improve the performance and life of the part.

[0056] The method of the present invention has certain universality and can be extended to high-efficiency, low-damage, high-quality ultra-precision grinding of small-caliber (φ20-φ50mm) rotating parts with a minimum surface curvature radius of 2mm. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A flow chart of a method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding using a hemispherical resonator in an embodiment of the present invention;

[0058] Figure 2 Schematic diagram of the structure of the processing equipment in an embodiment of the present invention;

[0059] Figure 3 Schematic diagram of the motion trajectory of the grinding wheel in an embodiment of the present invention;

[0060] Figure 4 Schematic diagram of the influence of abrasive particle size on the depth of subsurface damage of fused quartz in an embodiment of the present invention;

[0061] Figure 5 is a response surface diagram of subsurface damage depth in an embodiment of the present invention;

[0062] Figure 6 Schematic diagram of subsurface damage depth measurement of the outer sphere of a hemispherical resonator in an embodiment of the present invention.

[0063] Description of reference numerals:

[0064] 1-C-axis turntable, 2-U-axis connecting frame, 3, V-axis, 4-grinding wheel spindle fixing frame, 5-grinding wheel spindle, 6-ball head grinding wheel, 7-horizontal worktable, 8-workpiece spindle protection cover, 9-processed workpiece, 10-workpiece spindle, 11-U-axis protection cover, 12-U-axis. DETAILED DESCRIPTION

[0065] In the description of the present invention, it should be noted that the terminology in each embodiment, such as "up", "down", "front", "back", "left", "right", etc., which indicate directions, are only for simplifying the description of the positional relationship based on the drawings in the specification, and do not mean that the referred elements and devices must be operated in accordance with the specific directions and defined operations and methods and structures in the specification. Such directional nouns do not constitute a limitation to the present invention.

[0066] In the description of the present invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of the present invention are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly specifying the number of the technical features indicated. Therefore, a feature specified as "first," "second," or "third" may explicitly or implicitly include one or more of such features.

[0067] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0068] Specific implementation plan 1: Figure 1 As shown, the present invention provides a method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding using a hemispherical resonator, comprising the following steps:

[0069] S1. Using the diamond abrasive grain size of the ball-end grinding wheel as the variable, a single-factor experiment was conducted on the workpiece.

[0070] S2. Measure the subsurface damage depth of the workpiece under different diamond abrasive grain sizes. Taking the minimum subsurface damage depth of the workpiece as the constraint and taking high-efficiency processing into consideration, determine the optimal grinding wheel abrasive grain size for machining hemispherical resonators.

[0071] S3. Based on the determined optimal grinding wheel abrasive grain size, a central composite experimental design method was used. The process parameters to be optimized were used as central composite design factors, and the subsurface damage depth was used as the response indicator to design a central composite experimental plan. A central composite experiment was conducted to measure the subsurface damage depth of the workpiece under each set of process parameters, and a response surface model of the subsurface damage depth was established.

[0072] S4. Based on the established response surface model of subsurface damage depth, the process parameters and their ranges that affect the workpiece surface damage are determined with high efficiency and low subsurface damage depth as constraints;

[0073] S5, dividing the machining process into a high-efficiency grinding stage and a low-damage grinding stage, measuring the initial subsurface damage of the workpiece blank, determining the process parameters of the high-efficiency grinding stage based on the process parameters and their ranges affecting the workpiece surface damage obtained in S4, and determining the number of grinding times under each process parameter based on the initial damage measurement results of the workpiece blank;

[0074] Based on the process parameters and their ranges that affect the workpiece surface damage obtained by S4, the process parameters of the low-damage grinding stage are determined, and grinding experiments are carried out to measure the sub-surface damage depth of the workpiece under different process parameters. A damage suppression model is established based on the superposition effect of damage to control the remaining theoretical sub-surface damage depth in the low-damage grinding stage to be less than or equal to the damage depth under the current grinding process parameters, so as to determine the number of grinding times under various process parameters, and finally obtain the small-diameter ball head grinding wheel grinding process path for high-efficiency and low-damage grinding with a hemispherical resonator.

[0075] In this implementation, the machining process is divided into a high-efficiency grinding stage and a low-damage grinding stage. The goal of the high-efficiency grinding stage is to perform finishing grinding to remove initial subsurface damage on the workpiece blank, as well as errors such as coaxiality and uneven wall thickness caused by eccentricity when the workpiece is clamped on the spindle. The goal of the low-damage grinding stage is to remove subsurface damage in the high-efficiency grinding stage.

[0076] like Figure 2 As shown, the equipment used in this embodiment is the existing technology: an ultra-precision grinding device with a grinding wheel spindle placed obliquely and capable of rotating in space (application number: CN201710186959.2). The device is a four-axis linkage processing machine tool, including three linear moving axes and a C-axis turntable 1, as well as a grinding wheel spindle 5 and a workpiece spindle 10. The three linear moving axes are an X-axis linear unit, a Y-axis linear unit, and a Z-axis linear unit. The X-axis linear unit and the Y-axis linear unit are controlled by a control system to realize the linear movement of the horizontal worktable 7 along the X-axis direction and the Y-axis direction. The X-axis direction and the Y-axis direction are both horizontal directions. The Z-axis linear unit is controlled to realize the grinding wheel spindle 5 along the Z-axis. The C-axis turret 1 is used to realize the rotational movement of the grinding wheel spindle 5 along the Z axis. The ball-end grinding wheel 6 is installed at the output end of the grinding wheel spindle 5 through a precision chuck to realize high-speed rotation during processing. The angle between the grinding wheel spindle 5 and the horizontal plane is 40°. The grinding wheel spindle 5 is suspended and installed below the U-axis 12 through the grinding wheel spindle fixing frame 4, and the U-axis 12 is provided with a U-axis protective cover 11. The U-axis 12 is rigidly connected to the bottom of the C-axis turret 1 through the U-axis connecting frame 2. The V-axis 3 is installed below the C-axis turret 1. The lower end of the V-axis 3 is connected to the grinding wheel spindle fixing frame 4. The grinding wheel spindle 5 is fine-tuned in the Y-axis and X-axis directions through the U-axis 12 and the V-axis 3. The workpiece spindle 10 is provided with a workpiece spindle protective cover 8 and is installed on the upper surface of the horizontal workbench 7 through the workpiece spindle protective cover 8.

[0077] like Figure 3As shown in the figure, the motion trajectory of the grinding wheel is divided into 7 segments: AB, BC, CD, DE, EF, FG, and GH. The ball-end grinding wheel starts from point A. The AB segment is the machining trajectory of the inner rod; the BC segment is the machining trajectory of the transition fillet between the inner rod and the inner sphere; the CD segment is the machining trajectory of the inner sphere with the transition fillet boundary as the starting point; the DE segment is the machining trajectory of the connecting part of the inner and outer spheres; the EF segment is the machining trajectory of the outer sphere; the FG segment is the machining trajectory of the transition fillet between the outer sphere and the outer rod; and the GH segment is the machining trajectory of the outer rod.

[0078] During grinding, the relative grinding speed of the workpiece and the grinding wheel is adjusted by adjusting the rotational speed of the workpiece spindle 10 and the grinding wheel spindle 5. The feed speed of the workpiece and the grinding wheel is adjusted by controlling the movement speed of the horizontal worktable 7. The machine tool motion system completes the feed movement of the ball-end grinding wheel 6 by controlling the size of the tool radius compensation value, thereby adjusting the grinding depth. For the feed of the arc machining profile, the unshifted arc machining profile trajectory is offset by the size of the tool compensation value along the direction of the line connecting the arc center point and all points on the arc segment; for the feed of the straight line machining profile, the unshifted straight line machining profile trajectory is offset by the size of the tool compensation value in the direction close to the workpiece entity. The machine tool motion system controls the horizontal worktable to move along the X-axis and Y-axis directions of the machine tool, and realizes the feed of the ball-end grinding wheel by changing the position of the workpiece relative to the ball-end grinding wheel.

[0079] Specific implementation scheme 2: In S2, the optimal grinding wheel abrasive grain size for processing the hemispherical resonator is determined to be 5-7 μm. The rest of this implementation scheme is the same as the specific implementation scheme 1.

[0080] Because hemispherical resonators are expensive, high-purity fused quartz glass rods, the same material as the hemispherical resonators, were used as test workpieces for the experiments. S1 used ball-end grinding wheels with diamond grit sizes of W3, W7 (grinding wheel grit size of 5-7 μm), and W20, respectively. The machining parameters were: workpiece speed of 30 rpm, grinding wheel speed of 71,000 rpm, and feed rate of 30 μm / s. Grinding wheel characteristics were verified using grinding depths of 0.5 μm, 1 μm, 1.5 μm, and 2 μm. Each glass rod was ground for a length of 20 mm, for a total grinding depth of 30 μm.

[0081] like Figure 4As shown in the figure, a comparison of the machining quality of fused quartz workpieces produced by the W3 and W7 ball-end grinding wheels reveals that while the W3 ball-end grinding wheel produces superior machining quality than the W7 ball-end grinding wheel, the subsurface damage produced by the two grinding wheels is comparable and at the same level. The W7 ball-end grinding wheel allows for a relatively large grinding depth, significantly reducing grinding time. Therefore, the optimal grinding wheel grain size for machining hemispherical resonators is determined to be 5-7 μm. Furthermore, under the same process parameters, the subsurface damage depth of the fused quartz material increases with increasing grinding depth, demonstrating stable grinding wheel characteristics.

[0082] Specific implementation plan three: The process parameters to be optimized in S3 include: grinding speed v s , grinding depth a p , feed speed f. The rest of this embodiment is the same as the first embodiment.

[0083] Specific implementation plan 4: S3 includes the following processes:

[0084] S31, determine the grinding speed v s , grinding depth a p , the range of each process parameter of feed speed f, based on the determined optimal grinding wheel abrasive size, the central composite experimental design (CCD) method is adopted, the process parameters to be optimized are used as central composite design factors, and the subsurface damage depth is used as the response index to design the central composite experimental plan and carry out central composite experiments;

[0085] S32, measuring the subsurface damage depth under each set of process parameters in the experimental plan;

[0086] S33. The measured subsurface damage depth data are regressed using the least squares method to establish a response surface of the subsurface damage depth in the form of:

[0087]

[0088] Where y represents the subsurface damage depth, x i , x j represents the independent variable, β i Representation factor x i The corresponding first-order effect, β ij Represents different factors x i and x j The interaction between β ii Representation factor x i The quadratic term of k represents the number of factors; the coefficients of each item of the second-order response surface model are obtained using the least squares algorithm. The rest of this implementation plan is the same as the specific implementation plan three.

[0089] In this embodiment, a small-diameter ball-end grinding wheel is used for grinding the hemispherical resonator. The diameter of the grinding wheel is only 3.8 mm. Therefore, a smaller grinding depth and a suitable feed speed are required to achieve stable and controllable grinding of the hemispherical resonator. According to the processing characteristics of such parts and the grinding capacity of the small-diameter ball-end grinding wheel, the grinding speed v shown in Table 1 is determined. s , grinding depth a p , the range of feed speed f; using Design-Expert software, a three-factor, five-level central composite design scheme (Table 2) was designed, with the process parameters to be optimized as central composite design factors and the subsurface damage depth as the response indicator. Central composite experiments were conducted, with the workpiece speed set to 30 rpm and the grinding wheel speed adjusted accordingly to the grinding speed. The grinding length of each glass rod was 20 mm, and the total grinding depth was 30 μm.

[0090] The subsurface damage depth of the workpiece under each set of process parameters in the experimental scheme was measured, and the subsurface damage depth results in Table 2 were obtained;

[0091] The least squares method is used to perform regression processing on the measured subsurface damage depth data, and the stress surface model result is:

[0092]

[0093] The variance analysis of the corresponding surface model was performed, and the R 2 It is 0.9851, indicating that the accuracy of the model is high. The established response surface model can well reflect the functional relationship between the response value and the grinding parameter variable.

[0094] Table 1

[0095]

[0096] Table 2

[0097]

[0098]

[0099] Specific Implementation Plan 5: The process parameters and their ranges that affect workpiece surface damage are determined as follows: feed rate: 30μm / s to 40μm / s, grinding speed: 14m / s, and a gradually decreasing grinding depth is used during the low-damage grinding stage. This implementation plan is otherwise identical to Specific Implementation Plan 4.

[0100] In this embodiment, based on the corresponding surface model established, the following is drawn: Figure 5 The response surface plot of the subsurface damage depth is shown in Figure 5It can be seen that the interaction between grinding depth and feed rate is the strongest, confirming that grinding depth and feed rate are the key process parameters influencing workpiece surface damage. As can be seen from the figure, when the grinding speed is 10 m / s and the grinding depth is 1 μm, the SSD depth increases by approximately 4 μm even when the feed rate increases from 10 μm / s to 50 μm / s. However, when the grinding speed is 10 m / s and the grinding depth is 5 μm, the SSD depth changes dramatically with increasing grinding depth. Therefore, it can be concluded that when the grinding depth is small, increasing the feed rate can not only shorten the processing time but also maintain a low SSD depth. However, if the feed rate is too fast, grinding lines will form. These grinding lines are the source of spatial frequency error in the optical component surface, and this intermediate spatial frequency error is difficult to remove during the subsequent polishing process. Therefore, a feed rate range of 30μm / s to 40μm / s was determined to achieve higher machining efficiency and lower SSD damage depth. A higher grinding speed resulted in lower subsurface damage depth, so a grinding speed of 14m / s and a grinding depth of 0.5μm to 5μm were determined. A combination of high speed, large depth of cut, and medium-to-high feed rates can be employed in the subsequent high-efficiency grinding stage, while a combination of high speed, small depth of cut, and medium-to-low feed rates can be employed in the low-damage grinding stage.

[0101] Specific implementation scheme six: The damage inhibition model described in S5 is:

[0102]

[0103] Where, SSD(a pi ,v si ,f i ,d gi ) is the subsurface damage depth corresponding to the current grinding process parameters, SSD init is the initial subsurface damage depth of the workpiece, a pi The other aspects of this embodiment are the same as those of the first embodiment.

[0104] Specific implementation plan seven: The process path for the efficient grinding stage in S5 is as follows:

[0105] Stage I: grinding wheel speed 71000r / min, workpiece speed 30r / min, grinding depth 5μm, feed speed 40μm / s, grinding until full surface grinding is completed;

[0106] Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 40 μm / s, 6 grinding passes;

[0107] Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 30 μm / s, grinding 2 times;

[0108] The process path for the low-damage grinding stage is formulated as follows:

[0109] Stage I: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 2 μm, feed speed 30 μm / s, grinding 2 times;

[0110] Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 1 μm, feed speed 30 μm / s, grinding 2 times;

[0111] Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.5 μm, feed speed 30 μm / s, 1 grinding pass;

[0112] Stage IV: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.1 μm, feed speed 30 μm / s, 1 grinding pass;

[0113] Stage V: Grinding wheel speed 71000 r / min, workpiece speed 30 r / min, grinding depth 0 μm, feed rate 30 μm / s, grinding 1 time. The rest of this embodiment is the same as the specific embodiment 5.

[0114] In this embodiment: First, the initial subsurface damage of the outer surface of the workpiece blank is measured. The results are shown in Table 3. From the measurement results, it can be seen that the initial subsurface damage of the workpiece blank is about 40 μm.

[0115] Table 3

[0116]

[0117] Since the greater the grinding speed, the smaller the subsurface damage depth, the optimal grinding speed is determined to be 4m / s; the current maximum speed of the grinding wheel spindle is 80000r / min, so the workpiece spindle speed is set to 30r / min and the grinding wheel spindle speed is set to 71000r / min.

[0118] Developing a process route for an efficient grinding phase includes:

[0119] Since the initial subsurface damage is about 40μm, a grinding depth of 5μm is used for grinding. On the basis of precise shaping, it is necessary to continue grinding for 8 times or more. Therefore, the efficient grinding stage is divided into three stages:

[0120] In stage I, the workpiece was reshaped by grinding on the full surface of the hemispherical resonator using a feed rate of 40 μm / s and a grinding depth of 5 μm;

[0121] Phase II was ground 6 times with a feed rate of 40 μm / s and a grinding depth of 5 μm;

[0122] In stage III, the material was ground twice at a feed rate of 30 μm / s and a grinding depth of 5 μm.

[0123] Development of process path for low damage grinding stage:

[0124] As shown in Table 4, the grinding experiments were carried out using a W7 diamond ball grinding wheel with the workpiece speed set to 30 r / min, the grinding wheel speed set to 71000 r / min, the feed rate set to 30 μm / s, and the grinding depths set to 0.5 μm, 1 μm, 2 μm, 3 μm, 4 μm, and 5 μm, respectively. The subsurface damage depth of the fused quartz material under each experimental scheme was measured, and the results are shown in Table 4.

[0125] Table 4

[0126]

[0127] As shown in Table 4, in the previous process (stage III in the high-efficiency grinding stage), the subsurface damage depth of the fused quartz material processed at a feed rate of 30 μm / s and a grinding depth of 5 μm is 6.483 μm. When grinding twice with a grinding depth of 2 μm, the remaining theoretical damage layer depth is 2.483 μm, which is smaller than the subsurface damage depth of 4.217 μm at a feed rate of 30 μm / s and a grinding depth of 2 μm shown in Table 4. Therefore, the number of grinding times corresponding to a grinding depth of 2 μm is 2;

[0128] In the previous process, the subsurface damage depth of the fused quartz material was 4.217 μm when the feed rate was 30 μm / s and the grinding depth was 2 μm. When the grinding depth was 1 μm and the grinding was repeated once, the remaining theoretical damage layer depth was 3.217 μm, which was smaller than the subsurface damage depth of 3.798 μm at the feed rate of 30 μm / s and the grinding depth of 1 μm shown in Table 4. Therefore, the number of grinding times corresponding to the grinding depth of 1 μm was 1;

[0129] In the previous process, the subsurface damage depth of the fused quartz material was 3.798 μm when the feed rate was 30 μm / s and the grinding depth was 1 μm. When the grinding depth was 0.5 μm and ground once, the remaining theoretical damage layer depth was 3.298 μm, which was smaller than the subsurface damage depth of 3.665 μm at the feed rate of 30 μm / s and the grinding depth of 0.5 μm shown in Table 4. Therefore, the number of grinding times corresponding to the grinding depth of 0.5 μm was 1;

[0130] Keeping the feed rate unchanged at 30 μm / s, grinding was performed once with a grinding depth of 0.1 μm and 0 μm respectively for finishing processing to reduce the surface roughness of the workpiece.

[0131] Finally, a small-diameter ball-end grinding wheel grinding path with high efficiency and low damage of hemispherical resonator is obtained.

[0132] The above high-efficiency and low-damage grinding process is used to perform ultra-precision grinding of the hemispherical resonator and compared with the existing processing technology, namely:

[0133] The grinding wheel speed is 71000r / min, the workpiece speed is 30r / min, and the grinding process parameters at each stage are:

[0134] 1. Grinding depth 5μm, feed speed 30μm / s, continue grinding 8 times after the entire surface is ground;

[0135] 2. Grinding depth 2μm, feed speed 30μm / s, grinding 4 times;

[0136] 3. Grinding depth 1μm, feed speed 30μm / s, grinding 6 times;

[0137] 4. Grinding depth 0.5 μm, feed speed 30 μm / s, grinding 8 times.

[0138] The process route of this implementation scheme shortens the grinding processing time from 24 hours to 16 hours, reducing the processing time by 33.3%. The sub-surface damage depth of the outer sphere of the hemispherical resonator is measured to be 2.379μm, which is much lower than the sub-surface damage depth of the blank of 39.016μm. The results show that the grinding process route provided by the present invention achieves efficient, low-damage, and high-quality processing of the hemispherical resonator.

[0139] Specific implementation plan eight: Figure 6 As shown in FIG, the method for measuring subsurface damage of a workpiece includes the following steps:

[0140] Step 1: Using the selected polishing process parameters, magnetorheological single-point polishing is performed on the sidewall surface of the component to form polishing spots;

[0141] Step 2: Cleaning and etching the polished workpiece;

[0142] Step 3: measuring the three-dimensional profile of the polishing spot, and intercepting its two-dimensional profile to obtain the cross-sectional profile of the polishing spot;

[0143] Step 4: Measure the horizontal distance D between the crack vanishing point in the polishing area and the polishing boundary line, and determine the position of the corresponding crack vanishing point on the cross-sectional profile of the polishing spot according to the polishing boundary line;

[0144] Step 5: Using the contour data of the grinding area, the profile of the removed material is reconstructed based on the cross-sectional profile of the polishing spot to obtain a fitted profile curve of the removed material. The shortest distance between the crack vanishing point on the cross-sectional profile of the polishing spot and the fitted profile curve of the removed material is calculated to obtain the subsurface damage depth of the workpiece. This embodiment is otherwise identical to the first embodiment.

[0145] In this embodiment: for the polishing of a hemispherical resonator, the part is stationary during the process and the morphology of the polishing area is a polishing spot; the method of this embodiment can be used to measure the sub-surface damage depth of a small-diameter (φ20-φ50mm) rotating workpiece with a small face curvature radius of 2mm.

[0146] This embodiment can also be used for polishing fused silica glass rods. During the process, the part rotates and the polishing area is a polishing ring surrounding the side wall of the workpiece, and the sub-surface damage depth of the workpiece is measured.

[0147] In step 2, the polished workpiece is cleaned and etched, which includes the following steps:

[0148] Use deionized water, dilute hydrochloric acid, and alcohol to clean the magnetorheological fluid remaining on the surface of the workpiece after polishing;

[0149] Immersing the sample in an etching solution containing 1% HF and 15% NH4F by mass for 12 minutes to expose subsurface cracks covered by the polished hydrolyzed layer;

[0150] After etching, the workpiece surface was cleaned with deionized water and anhydrous ethanol to remove the residual acid on the surface.

[0151] In step 3, a white light interferometer is used to measure the three-dimensional topography profile of the polishing spot.

[0152] Specific embodiment 9: The polishing process parameters in step 1 are: polishing head speed 7000 r / min, polishing gap 80 μm, polishing time 15 to 20 minutes. The rest of this embodiment is the same as specific embodiment 8.

[0153] Specific implementation plan 10: Figure 6 As shown, the fitting contour curve of the removed material in step 5 is:

[0154]

[0155] Among them, x i and y i is the coordinate of point i on the fitting contour of the removed material, g(x,y) is the curve equation of the fitting contour of the removed material, R is the radius of the fitting contour, x o and y o is the center of the fitting circle;

[0156] The relationship between the crack vanishing point and the polishing junction point on the cross-sectional contour line of the polishing spot is:

[0157] x cv =x pi +D

[0158] Among them, x cv and x pi are the horizontal coordinates of the crack vanishing point and the polishing junction point, respectively;

[0159] The shortest distance between the crack vanishing point on the polishing spot cross-sectional profile and the fitted contour curve of the removed material is calculated as:

[0160]

[0161] Among them, x c and y c is the intersection of the line connecting the crack vanishing point and the center of the fitting circle and the fitting circle, that is:

[0162] The rest of this implementation plan is the same as the specific implementation plan eight.

[0163] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel with high efficiency and low damage of a hemispherical resonator, characterized in that: The steps include: S1. Using the diamond abrasive grain size of the ball-end grinding wheel as the variable, a single-factor experiment was conducted on the workpiece. S2. Measure the subsurface damage depth of the workpiece under different diamond abrasive grain sizes. Taking the minimum subsurface damage depth of the workpiece as the constraint and taking high-efficiency processing into consideration, determine the optimal grinding wheel abrasive grain size for machining hemispherical resonators. S3. Based on the determined optimal grinding wheel abrasive grain size, a central composite experimental design method was used. The process parameters to be optimized were used as central composite design factors, and the subsurface damage depth was used as the response indicator to design a central composite experimental plan. A central composite experiment was conducted to measure the subsurface damage depth of the workpiece under each set of process parameters, and a response surface model of the subsurface damage depth was established. S4. Based on the established response surface model of subsurface damage depth, the process parameters and their ranges that affect the workpiece surface damage are determined with high efficiency and low subsurface damage depth as constraints; S5, dividing the machining process into a high-efficiency grinding stage and a low-damage grinding stage, measuring the initial subsurface damage of the workpiece blank, determining the process parameters of the high-efficiency grinding stage based on the process parameters and their ranges affecting the workpiece surface damage obtained in S4, and determining the number of grinding times under each process parameter based on the initial damage measurement results of the workpiece blank; Based on the process parameters and their ranges that affect the workpiece surface damage obtained in S4, the process parameters for the low-damage grinding stage were determined, and grinding experiments were carried out to measure the subsurface damage depth of the workpiece under different process parameters. A damage suppression model was established based on the superposition effect of damage to control the remaining theoretical subsurface damage depth in the low-damage grinding stage to be less than or equal to the damage depth under the current grinding process parameters. This was used to determine the number of grinding passes under each process parameter, and ultimately, a small-diameter ball-end grinding wheel grinding path for high-efficiency and low-damage grinding with a hemispherical resonator was obtained. The damage suppression model described in S5 is: Where, SSD(a pi , v si , f i , d gi ) is the subsurface damage depth corresponding to the current grinding process parameters, SSD init is the initial subsurface damage depth of the workpiece, a pi is the grinding depth corresponding to the current process.

2. The method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 1 is characterized in that: In S2, it is determined that the optimal grinding wheel grain size for machining hemispherical resonators is 5-7 μm.

3. The method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 1, characterized in that: The process parameters to be optimized in S3 include: grinding speed v s , grinding depth a p , feed speed f.

4. The method for optimizing the grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 3 is characterized in that: S3 includes the following processes: S31, determine the grinding speed v s , grinding depth a p , the range of each process parameter of feed speed f, based on the determined optimal grinding wheel abrasive size, the central composite experimental design (CCD) method is adopted, the process parameters to be optimized are used as central composite design factors, and the subsurface damage depth is used as the response index to design the central composite experimental plan and carry out central composite experiments; S32, measuring the subsurface damage depth under each set of process parameters in the experimental plan; S33. The measured subsurface damage depth data are regressed using the least squares method to establish a response surface of the subsurface damage depth in the form of: Where y represents the subsurface damage depth, x i , x j represents the independent variable, β i Representation factor x i The corresponding first-order effect, β ij Represents different factors x i and x j The interaction between β ii Representation factor x i The quadratic term influence is taken into account, k represents the number of factors; the least squares algorithm is used to obtain the coefficients of the second-order response surface model.

5. The method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 4 is characterized in that: The process parameters and their ranges that affect the surface damage of the workpiece are determined as follows: feed speed: 30μm / s~40μm / s, grinding speed: 14m / s, and the processing method of gradually decreasing grinding depth is adopted in the low-damage grinding stage.

6. The method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 1, characterized in that: The process path for the efficient grinding stage in S5 is: Stage I: grinding wheel speed 71000r / min, workpiece speed 30r / min, grinding depth 5μm, feed speed 40μm / s, grinding until full surface grinding is completed; Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 40 μm / s, 6 grinding passes; Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 5 μm, feed speed 30 μm / s, grinding 2 times; The process path for the low-damage grinding stage is formulated as follows: Stage I: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 2 μm, feed speed 30 μm / s, grinding 2 times; Stage II: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 1 μm, feed speed 30 μm / s, grinding 2 times; Stage III: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.5 μm, feed speed 30 μm / s, 1 grinding pass; Stage IV: grinding wheel speed 71000 rpm, workpiece speed 30 rpm, grinding depth 0.1 μm, feed speed 30 μm / s, 1 grinding pass; Stage V: grinding wheel speed 71000 r / min, workpiece speed 30 r / min, grinding depth 0 μm, feed speed 30 μm / s, grinding 1 time.

7. The method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 1, characterized in that: The method for measuring subsurface damage of a workpiece includes the following steps: Step 1: Perform magnetorheological single-point polishing on the sidewall surface of the workpiece using the selected polishing process parameters to form polishing spots; Step 2: Cleaning and etching the polished workpiece; Step 3: measuring the three-dimensional profile of the polishing spot, and intercepting its two-dimensional profile to obtain the cross-sectional profile of the polishing spot; Step 4: Measure the horizontal distance D between the crack vanishing point in the polishing area and the polishing boundary line, and determine the position of the corresponding crack vanishing point on the cross-sectional profile of the polishing spot according to the polishing boundary line; Step 5: Using the contour data of the grinding area, the contour of the removed material is fitted and reconstructed based on the cross-sectional contour of the polishing spot to obtain the fitted contour curve of the removed material. The shortest distance from the crack vanishing point on the cross-sectional contour of the polishing spot to the fitted contour curve of the removed material is calculated to obtain the sub-surface damage depth of the workpiece.

8. The method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 7, characterized in that: The polishing process parameters in step 1 are: polishing head speed 7000 r / min, polishing gap 80 μm, and polishing time 15 to 20 min.

9. The method for optimizing grinding process parameters of a small-diameter ball-end grinding wheel for high-efficiency and low-damage grinding of a hemispherical resonator according to claim 7, characterized in that: The fitting contour curve of the removed material in step 5 is: Among them, x i and y i is the coordinate of point i on the fitting contour of the removed material, g(x,y) is the curve equation of the fitting contour of the removed material, R is the radius of the fitting contour, x o and y o is the center of the fitting circle; The relationship between the crack vanishing point and the polishing junction point on the cross-sectional contour line of the polishing spot is: x cv =x pi +D Among them, x cv and x pi are the horizontal coordinates of the crack vanishing point and the polishing junction point, respectively; The shortest distance between the crack vanishing point on the polishing spot cross-sectional profile and the fitted contour curve of the removed material is calculated as: Among them, x c and y c is the intersection of the line connecting the crack vanishing point and the center of the fitting circle and the fitting circle, that is:

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