Design method of a milling and grinding wheel and an elastic clamp

Abstract

The application discloses a design method of a milling and grinding wheel and an elastic clamp, and relates to the technical field of optical part machining. min 、 h min 、 t, D t and R; step two, judging whether h=2r is established, if yes, entering step three, otherwise, entering step four; step three, obtaining a first value range of r, and selecting r0, D0 and a designed value of a clamp groove depth; step four, judging whether r is greater than or equal to 0.5D, if yes, entering step five, otherwise, entering step six; step five, obtaining a second value range of r, and selecting r0, D0, h0 and a designed value of a clamp groove depth; step six, obtaining a third value range of r, and selecting r0, D0, h0 and a designed value of a clamp groove depth; the method avoids that the clamp is worn by the grinding wheel during grinding wheel machining by theoretically designing the structure of the grinding wheel and the clamp.

Description

Technical Field

[0001] This invention belongs to the field of optical component processing technology, specifically relating to a design method for milling grinding wheels and elastic clamps. Background Technology

[0002] With the rapid development of the smartphone and autonomous driving industries, the demand for small-diameter optical components is increasing, which also places new demands on the processing efficiency of optical components. Milling (generating process) is one of the important processes in the processing of optical components. The quality of the optical components after milling directly affects the product quality and production efficiency. Therefore, reasonable design of grinding wheels and fixtures is particularly important.

[0003] In the milling and grinding of optical components, flexible clamps can precisely fix the optical components and absorb the vibrations generated during the processing. Furthermore, flexible clamps are characterized by low cost, long service life, high versatility, and convenient component installation and disassembly. Therefore, they are widely used in the milling and grinding production of optical components. However, in the milling and grinding of small-diameter convex optical components, especially when the radius of curvature of the machined surface is small, it is difficult to quickly and appropriately select the size of the grinding wheel or flexible clamp. This can easily lead to wear on the grinding wheel and clamps, affecting their service life and the accuracy of the machined parts. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for milling grinding wheels and elastic clamps that is simple in structure and reasonable in design in order to solve the above-mentioned problems.

[0005] The present invention achieves the above objectives through the following technical solutions:

[0006] A design method for milling grinding wheels and elastic clamps includes the following steps:

[0007] Step 1: Collect the following information: The minimum radius of the arc on the end face of the grinding wheel is r. min The minimum thickness of the grinding wheel head is h. min The edge thickness t of the part, and the expected aperture D of the optical part after milling. t The radius of curvature R of the spherical surface of the optical component to be milled as expected;

[0008] Step 2: Determine if the thickness of the grinding wheel head is equal to twice the radius of the arc of the grinding wheel head end face. If it is equal, proceed to Step 3; otherwise, proceed to Step 4.

[0009] Step 3, at this time r min ≤r≤0.5D max According to D max With R, r, t, D t H minThe functional relationship is used to obtain inequality 1, and solving inequality 1 yields the first range of values ​​for r.

[0010] The design radius r0 of the arc at the end face of the grinding wheel head is selected. The design radius r0 of the arc at the end face of the grinding wheel head belongs to the first range of values ​​and satisfies r min ≤r≤0.5D max conditions;

[0011] Then select the design value D0 for the grinding wheel diameter;

[0012] Based on the maximum groove depth and R, r, t, D t The relationship between D and the maximum groove depth is used to calculate the maximum groove depth, and the design value of the groove depth is selected within the range of the maximum groove depth.

[0013] Step 4: Determine if r ≥ 0.5D. If yes, proceed to Step 5; otherwise, proceed to Step 6.

[0014] Step 5, r≥0.5D, D≥D min Therefore, 0.5D min ≤r, according to D min With R, r, D t H min The functional relationship is used to obtain inequality 2, and inequality 2 is solved to obtain the second range of values ​​for r;

[0015] The design radius r0 of the end face arc of the grinding wheel head is selected. The design radius r0 of the end face arc of the grinding wheel head is within the second range of values ​​and satisfies the condition r≥0.5D.

[0016] Then select the design value D0 for the grinding wheel diameter;

[0017] The design value h0 of the grinding wheel head thickness is selected to meet the following requirements. and the conditions h0≤D0;

[0018] Step 6: Since r < 0.5D, D ≤ D max Therefore r <D max According to D max With R, r, t, D t H min The functional relationship is used to obtain inequality 3, and solving inequality 3 yields the third range of values ​​for r.

[0019] The design radius r0 of the arc at the end face of the grinding wheel head is selected. The design radius r0 of the arc at the end face of the grinding wheel head belongs to the third range of values ​​and satisfies r min ≤r <D max ;

[0020] Then select the design value D0 for the grinding wheel diameter;

[0021] In this step, r0 and D0 are selected to satisfy the condition r0+R≥0.5D0;

[0022] The design value h0 of the grinding wheel head thickness is selected to meet the following requirements. and h min ≤h0≤2r0 condition.

[0023] Furthermore, the method for selecting the design value D0 of the grinding wheel diameter in step five is as follows: calculate the minimum value D of the grinding wheel diameter based on the design radius r0 of the arc of the grinding wheel head end face. min The maximum value D of the grinding wheel diameter max At the minimum value D of the grinding wheel diameter min The maximum value D of the grinding wheel diameter max The design value D0 of the grinding wheel diameter is selected from the available options. The design value D0 of the grinding wheel diameter must satisfy 2r0≥D0.

[0024] The method for selecting the design value D0 of the grinding wheel aperture in steps three and six is ​​as follows: calculate the minimum value D of the grinding wheel aperture based on the design radius r0 of the arc of the grinding wheel head end face. min The maximum value D of the grinding wheel diameter max At the minimum value D of the grinding wheel diameter min The maximum value D of the grinding wheel diameter max Choose the design value D0 for the grinding wheel diameter, which must satisfy 2r0≤D0.

[0025] Furthermore, the initial value range of r is:

[0026] Furthermore, D max With R, r, t, D t H min The functional relationship is:

[0027]

[0028] Furthermore, calculate D min The formula is:

[0029]

[0030] Furthermore, the maximum value of the groove depth is related to R, r, t, and D. t The relationship between D and D is:

[0031]

[0032] Furthermore, inequality 1 is as follows:

[0033]

[0034] Furthermore, inequality 2 is as follows:

[0035]

[0036] Furthermore, inequality 3 is as follows:

[0037]

[0038] Furthermore, when the grinding wheel obtained according to the design method is used to mill optical parts, the spherical surface of the grinding wheel head is tangent to the glass spherical surface of the optical part being processed. At this time, the thickness h of the grinding wheel head satisfies the constraint condition h≥2rsinα.

[0039] The present invention has at least the following beneficial effects: Through the above-described six-step design method, and through theoretical calculations combined with actual production, when dealing with convex optical parts with thin edge thickness, small diameter, and small radius of curvature, the present invention can reasonably select the design values ​​of the radius r of the end face arc of the grinding wheel and the middle diameter D of the grinding wheel according to the actual application conditions. Furthermore, a reasonable selection is made for the design value of the maximum clamping groove depth H'max of the fixture. This ensures that, under these conditions, the grinding wheel will not wear down the fixture when milling optical parts, thereby increasing the service life of the fixture, improving processing accuracy, and reducing production costs. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the milling principle for optical components in existing technology;

[0041] Figure 2 This is a comparative structural diagram of an elastic abrasive tool before and after wear in the prior art;

[0042] Figure 3 This is a flowchart of the design method for milling grinding wheels and elastic clamps provided by the present invention;

[0043] Figure 4 This is a schematic diagram of the milling principle for convex parts with the smallest grinding wheel diameter provided by the present invention;

[0044] Figure 5 This is a schematic diagram of the milling principle of convex parts when the groove depth is at its maximum, provided by the present invention.

[0045] Figure 6 This is a schematic diagram of the milled optical component provided by the present invention. Detailed Implementation

[0046] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0047] In existing technologies, the specific working principle of spherical milling for optical components is as follows: Figure 1 As shown, the diamond grinding wheel's cutting edge passes through the workpiece's vertex, and the grinding wheel's axis and the workpiece's axis intersect at point O, with an angle α between the two axes. The grinding wheel rotates at high speed around its own axis, while the workpiece rotates at low speed around its own axis. The envelope of this motion trajectory forms a sphere.

[0048] The radius of the sphere is related to the angle α between the two axes. Once the mold is selected, the mean diameter D... m The radius r of the end face arc is a constant. By adjusting different angles α, spherical surfaces with different radii R can be machined. The relationship between R and α is as follows:

[0049]

[0050] Conditions: ① The cutting edge of the diamond grinding wheel passes through the apex of the workpiece; ② The axis of the grinding wheel and the axis of the workpiece intersect at point O; ③ The included angle between the two axes is α; ④ The grinding wheel rotates at high speed around its own axis, and the workpiece rotates at low speed around its own axis.

[0051] Therefore, in actual production, for convex optical parts with thin edges, small diameters, and small radii of curvature, the values ​​of the mean diameter D and r of the milling wheel are entirely based on experience. Even slight deviations can easily lead to damage to the grinding wheel and the fixture. Figure 2 As shown, Figure 2 The left image is a schematic diagram of the unworn fixture structure, with the central area indicating the placement of optical components. Figure 2 The right figure shows a schematic diagram of the fixture structure after wear. A comparison reveals that if the values ​​of D and r are not properly selected, even a slight deviation will result in the groove-shaped wear shown in the diagram on the fixture. Damage to the fixture by the grinding wheel not only affects the fixture's service life but also impacts machining accuracy and increases machining costs.

[0052] To address the above issues, increase fixture lifespan, improve machining accuracy, and reduce production costs, please refer to [reference needed]. Figure 3 This invention provides a design method for milling grinding wheels and elastic clamps, comprising the following steps:

[0053] Step 1: Collect the following information: The minimum radius of the arc on the end face of the grinding wheel is r. min The minimum thickness of the grinding wheel head is h. min The edge thickness t of the part, and the expected aperture D of the optical part after milling. t The radius of curvature R of the spherical surface of the optical component to be milled as expected;

[0054] Step 2: Determine if the thickness of the grinding wheel head is equal to twice the radius of the arc of the grinding wheel head end face. If it is equal, proceed to Step 3; otherwise, proceed to Step 4.

[0055] Step 3, at this time r min ≤r≤0.5D max According to D max With R, r, t, D t H min The functional relationship is used to obtain inequality 1, and solving inequality 1 yields the first range of values ​​for r.

[0056] The design radius r0 of the arc at the end face of the grinding wheel head is selected. The design radius r0 of the arc at the end face of the grinding wheel head belongs to the first range of values ​​and satisfies r min ≤r≤0.5D max conditions;

[0057] Then select the design value D0 for the grinding wheel diameter;

[0058] Based on the maximum groove depth and R, r, t, D t The relationship between D and the maximum groove depth is used to calculate the maximum groove depth, and the design value of the groove depth is selected within the range of the maximum groove depth.

[0059] Step 4: Determine if r ≥ 0.5D. If yes, proceed to Step 5; otherwise, proceed to Step 6.

[0060] Step 5, r≥0.5D, D≥D min Therefore, 0.5D min ≤r, according to D min With R, r, D t H min The functional relationship is used to obtain inequality 2, and inequality 2 is solved to obtain the second range of values ​​for r;

[0061] The design radius r0 of the end face arc of the grinding wheel head is selected. The design radius r0 of the end face arc of the grinding wheel head is within the second range of values ​​and satisfies the condition r≥0.5D.

[0062] Then select the design value D0 for the grinding wheel diameter;

[0063] The design value h0 of the grinding wheel head thickness is selected to meet the following requirements. and the conditions h0≤D0;

[0064] Step 6: Since r < 0.5D, D ≤ D max Therefore r <D max According to D max With R, r, t, D t H min The functional relationship is used to obtain inequality 3, and solving inequality 3 yields the third range of values ​​for r.

[0065] The design radius r0 of the arc at the end face of the grinding wheel head is selected. The design radius r0 of the arc at the end face of the grinding wheel head belongs to the third range of values ​​and satisfies rmin ≤r <D max ;

[0066] Then select the design value D0 for the grinding wheel diameter;

[0067] In this step, r0 and D0 are selected to satisfy the condition r0+R≥0.5D0;

[0068] The design value h0 of the grinding wheel head thickness is selected to meet the following requirements. and h min ≤h0≤2r0 condition.

[0069] In the above embodiments, through theoretical calculations and combined with actual production, when dealing with convex optical parts with thin edge thickness, small diameter, and small radius of curvature, the design values ​​of the radius r of the end face of the grinding wheel and the middle diameter D of the grinding wheel can be reasonably selected. In addition, the design value of the maximum clamping groove depth H'max of the fixture is also reasonably selected, thereby ensuring that the fixture will not be worn when the optical parts are milled by the grinding wheel under these conditions, increasing the service life of the fixture, improving the processing accuracy, and reducing the production cost.

[0070] For example, see [link to relevant documentation]. Figure 4 This diagram illustrates the milling principle of convex optical components when the grinding wheel diameter is at its minimum. As shown, one side of the diamond grinding wheel head passes through the workpiece vertex, and the spherical surface of the other grinding wheel head is tangent to the edge of the spherical surface of the optical component. Alternatively, the line connecting the center of the optical component's sphere and the center of the grinding wheel head passes through the outermost edge of the optical component's sphere. In this case, the median diameter of the grinding wheel is the minimum value D. min Specifically, the minimum value D of the grinding wheel's mean diameter is calculated. min The formula is:

[0071]

[0072] From D min The expression shows that D min It is an increasing function of r.

[0073] Continue reading Figure 5 This is a schematic diagram of the milling principle for convex parts when the groove depth is at its maximum. At this point, the minimum value D of the grinding wheel's median diameter is calculated. min Maximum value of the clamping groove depth H max The expression is:

[0074]

[0075] Due to limitations in the mechanical properties, clamping stability, and firmness of the clamping material, it is assumed that the minimum depth H in actual use... minFor a specific value, when the groove depth is less than this value, the part will be subjected to tangential and directional forces from the grinding wheel during machining, causing it to fall out of the fixture, making normal machining impossible, or even resulting in adverse consequences. Therefore, the groove depth H needs to satisfy condition H max ≥H min .

[0076] Therefore, based on the aforementioned condition for satisfying the groove depth H, the inequality for r is obtained, that is, the initial range of values ​​for r:

[0077]

[0078] Based on the minimum groove depth H min When a specific value is taken, the corresponding grinding wheel mean diameter D can reach its maximum value. max Specifically, D max With R, r, t, D t H min The functional relationship is:

[0079]

[0080] For example, based on D min and D max The formula is used to obtain the maximum value of the groove depth in relation to R, r, t, and D. t The relationship between D and D is: The specific methods for obtaining it are as follows:

[0081] (1) According to D min and D max The expression yields the following range of values ​​for the grinding wheel's mean diameter D:

[0082]

[0083] (2) Take the derivative of ΔD with respect to r. When the derivative is 0,

[0084]

[0085] (3) When r is rd, ΔD has a maximum value, that is, the maximum range of values ​​for the grinding wheel's median diameter. For any selected value of D, the expression for the maximum groove depth H'max is:

[0086] Where t is the edge thickness of the optical component, and D t Let αD be the diameter of the milled part, R be the radius of curvature of the part, r be the radius of arc of the grinding wheel end face, D be the mean diameter of the grinding wheel, and αD be the diameter of the grinding wheel. min The minimum value D is taken for the grinding wheel's median diameter. min At this time, the angle between the grinding wheel axis and the workpiece axis is a constant.

[0087] It should be noted that αD min It only relates to the part dimensions. Due to αD min H' is a constant, t is a constant, and when r is selected, H' max It is a decreasing function of D. When D is selected, H' max It is an increasing function of r. Once r is chosen, although H' is uncertain... max The value of is determined, but its range can be specified. When D = D min H' max Take the maximum value when D = D max H' max Take the minimum value.

[0088] It should be noted that since the grinding wheel head can be designed in hemispherical or non-hemispherical shapes, each case needs to be analyzed separately. Therefore, in step two, it is necessary to determine whether the thickness h of the selected grinding wheel head is equal to twice the radius r of the arc of the grinding wheel head end face, and to carry out further design based on the determination result.

[0089] For example, when h = 2r, that is, under normal conditions, the thickness of the grinding wheel head (metal part) is equal to twice the radius r of the arc of the grinding wheel head end face (diamond wheel part). Due to the limitations of the mechanical properties of the diamond wheel material, it is assumed that the minimum radius of the arc of the grinding wheel head end face in actual use is r. min The minimum thickness of the grinding wheel head is h. min Both are specific values; the radius r of the arc at the end face of the grinding wheel head is less than r0. min When processing, the wear resistance is poor, the adhesion to the metal substrate is weak, and it is prone to breakage or detachment from the metal substrate, making normal processing impossible and even causing adverse consequences. Therefore, in use, the value range of r must meet the following conditions: r min ≤r≤0.5D.

[0090] Among them, because D min ≤D max , obtain r min ≤r≤0.5D max And according to D max With R, r, t, D t H min The functional relationship yields inequality 1. Solving inequality 1 gives the first range of values ​​for r. Inequality 1 is as follows:

[0091]

[0092] Combining inequalities That is, the initial range of values ​​for r is used to obtain the first range of values ​​for the radius r of the arc at the end face of the grinding wheel head. Here, both sides of the two inequalities regarding r are constants, thus obtaining a wider and more definite numerical range for r. Within the specific numerical range constrained by these two inequalities, a suitable r0 can be selected. It should be noted that when selecting r0, the relationship between r and ΔD and H' must also be considered. max The influence of the selected value is considered to determine that r0 is the optimal solution.

[0093] The method for selecting the design value D0 of the grinding wheel diameter includes the following steps: substituting r = r0 into D. min and D max The expression is derived, and based on r ≤ 0.5D, we obtain 2r0 ≤ D0 and D min ≤D0≤D max The constraint range is used to determine the design value D0 of the grinding wheel's center diameter D; where, once r0 is determined, then D... min With D max Let it be a constant, such that at a given D min With D max There exists a D0 greater than or equal to 2r0, i.e., D0 ≥ 2r0, since r ≤ 0.5D max As long as r simultaneously satisfies both the initial value range and the first value range, it is certain that it can be between 2r0 and D. max Find D0 such that 2r0 ≤ D0; moreover, when choosing D0, we should also consider H' max The impact of the value;

[0094] And the maximum groove depth H' when the grinding wheel's median diameter is D0 max The steps for selecting the values ​​include: substituting r0 and D0 into H' max The expression is used to calculate the design value of the corresponding maximum groove depth.

[0095] When designing according to the above method, wear of the elastic clamp by the grinding wheel can be avoided, while ensuring that the clamp has sufficient groove depth, and, according to H' max The value of this value can also provide technicians with a reference for the maximum groove depth, so as to avoid the groove being too deep in actual processing, which would cause the elastic clamp to wear out during subsequent milling and grinding.

[0096] For example, when the grinding wheel head is not hemispherical, the thickness h of the grinding wheel head is not equal to the radius r of the arc of the end face of the grinding wheel head.

[0097] In step five, r ≥ 0.5D, and further based on r ≥ 0.5D ≥ 0.5D min According to D min With R, r, D t H minThe functional relationship yields inequality 2:

[0098]

[0099] And continue based on the initial range of values ​​for r. The solution yields the following second range of values ​​for r:

[0100]

[0101] Within the specific constraints mentioned above, the influence of r on the values ​​of ΔD and H'max can be comprehensively considered to select the design radius r0 of the arc of the grinding wheel head end face. The design radius r0 of the arc of the grinding wheel head end face belongs to the second value range and satisfies the condition r≥0.5D.

[0102] After r0 is determined, based on D min and D max The expression yields D. min and D max As a constant, and based on r≥0.5D, we derive 2r0≥D0 and D min ≤D0≤D max The constraint range is such that, therefore, as long as r simultaneously satisfies 2r≥D and D min ≤D≤D max The constraints can be applied to 2r0 and D. min Find D0 such that 2r0≥D0.

[0103] It should be noted that when selecting D0, its impact on H' should also be considered. max The influence of the value, and under the condition and h min Under the constraint ≤h≤D, obtain the constraint range of h. and h min ≤h≤D0, and within this constraint range, select and determine the appropriate design value h0 for the grinding wheel head thickness.

[0104] And the maximum groove depth H' when the grinding wheel's median diameter is D0 max The steps for determining the design value include: based on H' max The functional relationship expression between r0 and D0 is used to obtain the design value of the corresponding maximum groove depth.

[0105] Based on the above, it can be seen that under the conditions of h < 2r and r ≥ 0.5D, the structural design of the milling wheel and elastic clamp can effectively avoid the milling wheel from wearing the elastic clamp, while ensuring that the elastic clamp has sufficient clamping groove depth. Furthermore, based on the value of H'max, it can also provide technicians with a reference for the maximum clamping groove depth, so as to avoid the groove being too deep in actual processing, which would cause the milling wheel to wear the elastic clamp during subsequent milling processing.

[0106] In step six, since r < 0.5D, based on the constraints of r < 0.5D and r + R ≥ 0.5D, and further based on D... max With R, r, t, D t H min The functional relationship yields inequality 3:

[0107] And based on the initial range of values ​​for r The third range of values ​​for r is obtained by combining the results.

[0108] Obtain the constraint range of the radius r of the arc on the end face of the grinding wheel head under this condition, and select the design radius value r0 of the arc on the end face of the grinding wheel head. The design radius r0 of the arc on the end face of the grinding wheel head belongs to the third value range and satisfies r min ≤r <D max Then, based on this, the design value D0 of the grinding wheel's center diameter D, the design value h0 of the grinding wheel head thickness, and the maximum value H' of the groove depth when the grinding wheel's center diameter is D0 are selected and determined. max The design value.

[0109] Specifically, since r < 0.5D, then 2r < D, and h min ≤h≤D, h<2r, therefore h min ≤h≤2r, and Based on h < 2r, we get Solving the inequality, we get: r + R ≥ 0.5D.

[0110] Wherein, after r0 is determined, based on D min and D max The expression yields D. min and D max For a constant value, then in D min and D max Choose D0 that is greater than or equal to 2r0.

[0111] It should be noted that when selecting D0, its impact on H' should also be considered. max The influence of the values ​​of r and D, and when choosing r and D, it is also necessary to consider whether r and D satisfy the inequality: r + R ≥ 0.5D. Finally, in h min ≤h<2r0 and The design value h0 for the thickness of the grinding wheel head is selected from the given values.

[0112] The steps for determining the design value of the maximum groove depth H'max when the grinding wheel's median diameter is D0 include: based on H' max The functional relationship expression between r0 and D0 is used to obtain the design value of the corresponding maximum groove depth.

[0113] By determining r0, D0, and h0 through the above steps, and designing the resulting grinding wheel structure and elastic clamping fixture according to the selected r0, D0, and h0 using the above method, wear on the elastic clamping fixture can be avoided during milling. Simultaneously, it ensures that the clamping fixture has sufficient groove depth, enabling normal processing of optical components.

[0114] For example, such as Figure 6 The diagram shown is a schematic of the optical component after milling. The edge thickness of the component is t = 1.38 mm, and the diameter of the component is D. t =11.6mm, convex surface radius of curvature R = 10.485mm. Take the minimum value of the end face arc radius r. min =0.2mm, the minimum thickness of the grinding wheel head is h. min = 0.4mm, minimum groove depth H min =0.3mm.

[0115] Let t, D t H min r min Substitute R into the following inequality:

[0116]

[0117] Therefore: 0.2mm < r ≤ 6.47mm.

[0118] Differentiate ΔD with respect to r. When the derivative is 0, consider t and D. t H min r min Substitute R into the following formula:

[0119]

[0120] When rd = -6.25mm (the value of r when ΔD reaches its maximum value), ΔD reaches its maximum value. When r ranges from 0.2mm to 6.47mm, ΔD is a decreasing function of r. R = 10.485mm, and... When D is 6.47mm, min =D max When ΔD = 0, and r takes values ​​between 0.2 mm and 6.47 mm, ΔD is greater than or equal to zero.

[0121] When the thickness of the grinding wheel head is h = 2r, solve the inequality:

[0122]

[0123] Therefore, -3.2mm ≤ r ≤ 4.624mm. Combining this with 0.2mm < r ≤ 6.47mm, the constraint range for r is determined to be: 0.2mm < r ≤ 4.624mm.

[0124] Increasing the values ​​of ΔD and H'max appropriately provides greater adjustment flexibility during actual operation and process parameter adjustments. However, H'max is an increasing function of r, and when r ranges from 0.2 to 4.624 mm, ΔD is a decreasing function of r, making it impossible for both to reach their maximum values ​​simultaneously. Considering the durability of the grinding wheel, we assume that r0 = 1 mm (not unique; theoretically, any value between 0.2 and 4.624 mm can be selected), H'... max The value range is 0.3~1.213mm, ΔH' max =0.913mm, D ranges from 6.64 to 8.06mm and ΔD = 1.42mm.

[0125] When r0 = 1 mm, within the constraints of 6.64 mm ≤ D ≤ 8.06 mm and D ≥ 2r0 = 2 mm, the design value D0 of the grinding wheel's mean diameter D is selected and determined. Since H' max It is a decreasing function of D, and D should be chosen to be the minimum value of 6.64 mm, H' max The maximum value of 1.21mm is taken. However, in actual operation, a slight error in the longitudinal movement (or the part is machined to the upper tolerance while the grinding wheel is machined to the lower tolerance) may cause the edge of the part to not contact the grinding wheel, resulting in a non-perfect spherical surface. This makes it impossible to measure the radius of curvature of the machined surface online, and therefore impossible to adjust the process parameters based on the measured radius of curvature. Therefore, the value of D can be appropriately increased from 6.64mm. Assuming D = 7mm (not unique; theoretically, any value between 6.64 and 8.06mm can be selected), the maximum depth of the groove is: H' max = 0.997mm. Substitute D, r, and R into: The angle α between the grinding wheel axis and the workpiece axis is 17.75 degrees. This ensures that the groove depth during machining does not exceed H'. max =0.997mm. Through the above structural design of the milling wheel and the design of the groove depth of the elastic clamp, it can be ensured that the milling wheel does not wear the elastic clamp during milling, thereby increasing the service life of the clamp, improving the machining accuracy, and reducing the production cost.

[0126] When h < 2r, h satisfies the following constraint: h min Given h ≤ D, determine whether r ≥ 0.5D holds true based on the constraint condition h above.

[0127] When r ≥ 0.5D,

[0128] Let t, D t H min Substituting the parameters of R into the above inequality, we get: 4.26mm≤r≤6.47mm.

[0129] Appropriately increase ΔD and H' max The numerical value, in actual operation and adjustment of process parameters, has greater room for adjustment, but H' max ΔD is an increasing function of r. When r takes values ​​between 4.26 and 6.47 mm, ΔD is a decreasing function of r. It's impossible for both to simultaneously reach their maximum values. Assuming we choose r0 = 5 mm (not unique; theoretically, it can take any value between 4.26 and 6.47 mm), H' max The value range is 0.3~0.55mm, ΔH' max =0.25mm, the value range of D is 8.95~9.36mm and ΔD=0.41mm. Based on D0≤2r0=10mm and the value range of D: 8.95~9.36mm, consider H' max For the value, choose D0 = 9.2mm (not unique, theoretically any value between 8.95 and 9.36mm can be used), H' max =0.4mm. At this time, Choose h0 = 4mm.

[0130] Substitute the parameter values ​​r0 = 5mm, D0 = 9.2mm, and R = 10.485mm into the following values: The angle α between the grinding wheel shaft and the workpiece shaft is 17.29 degrees. At this point, the depth of the clamping groove during machining does not exceed H'. max =0.4mm, which prevents the grinding wheel from wearing down the fixture.

[0131] When r < 0.5D, solve the following inequality:

[0132]

[0133] The constraint range for r is determined to be 0.2 mm. <r<4.624mm。

[0134] Appropriately increase ΔD and H' max The numerical value, in actual operation and adjustment of process parameters, has greater room for adjustment, but H' max ΔD is an increasing function of r. When r takes values ​​between 0.2 and 4.624 mm, ΔD is a decreasing function of r. It's impossible for both to simultaneously reach their maximum values. Considering the durability of the grinding wheel, we assume r0 = 3.5 mm (not unique; theoretically, any value between 0.2 and 4.624 mm can be chosen). H' max The value range is 0.30~0.80mm, ΔH' max =0.5mm, D ranges from 8.08 to 8.90mm and ΔD = 0.82mm.

[0135] When r₀ = 3.5 mm is selected, the value range of D is 8.08 mm ≤ D ≤ 8.90 mm, and R = 10.485 mm, which always satisfies r + R ≥ 0.5D, and simultaneously satisfies D ≥ 2r₀ = 7 mm. Since H' max is a decreasing function of D, D should be selected as the minimum value 8.08 mm, and H' max takes the maximum value 0.80 mm. However, in actual operation, a slight error in the longitudinal movement amount (or when the part is processed to the upper tolerance and the grinding wheel is processed to the lower tolerance) is very likely to cause the edge of the part to not contact the grinding wheel, resulting in that the processed surface is not a complete spherical surface, and the on-line measurement of the curvature radius of the processed surface cannot be performed, so the process parameters cannot be adjusted according to the measured curvature radius. Therefore, the value of D can be appropriately increased on the basis of 8.08 mm. Assuming that D = 8.5 mm is selected (not unique, any value between 8.08 mm and 8.90 mm can be theoretically selected), the maximum depth of the clamping groove at this time is: H' max = 0.55 mm. According to H min ≤ h < 2r₀, select h₀ = 5 mm within the constraint range (not unique, 2.13 mm < h₀ < 7 mm). Substitute D = 8.5 mm, r = 3.5 mm, and R = 10.485 mm into to obtain that the included angle α between the grinding wheel shaft and the workpiece shaft is 17.70 degrees, and the depth of the clamping groove during processing does not exceed H' max = 0.55 mm. Through the above structural design of the milling-grinding wheel and the design of the clamping groove depth of the elastic fixture, the grinding wheel will not wear the fixture during milling-grinding processing, which increases the service life of the fixture, improves the processing precision and reduces the production cost.

[0136] The above-described examples only show several embodiments of the present invention, and the description thereof is relatively specific and detailed, but it should not be construed as limiting the scope of the patent of the present invention. It should be noted that, for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can be made, and these all belong to the protection scope of the present invention.

Claims

1. A design method for a milling grinding wheel and an elastic clamp, characterized in that, Includes the following steps: Step 1: Collect the following information: The minimum radius of the arc on the end face of the grinding wheel is... The minimum thickness of the grinding wheel head is The edge thickness t of the part, and the expected diameter of the optical part after milling. The radius of curvature R of the spherical surface of the optical component to be milled as expected; Step 2: Determine if the thickness of the grinding wheel head is equal to twice the radius of the arc of the grinding wheel head end face. If it is equal, proceed to Step 3; otherwise, proceed to Step 4. Step 3, at this time ,according to With R, r, t, , The functional relationship yields inequality 1. Solving inequality 1 provides the first range of values ​​for r, where r is the radius of the arc at the end face of the grinding wheel. This represents the maximum value of the grinding wheel's median diameter. To determine the minimum groove depth, the initial range of values ​​for r is: ; Select the design radius of the end face arc of the grinding wheel head. The design radius of the arc at the end face of the grinding wheel head It belongs to the first range of values ​​and satisfies conditions; Then select the design value for the grinding wheel diameter. The grinding wheel diameter refers to the center diameter of the grinding wheel; Based on the maximum groove depth and R, r, t, The relationship between D and the maximum value of the groove depth is used to calculate the maximum value of the groove depth, and the design value of the groove depth is selected within the range of the maximum value of the groove depth, where D is the middle diameter of the grinding wheel; Step 4: Determine if r ≥ 0.5D. If yes, proceed to Step 5; otherwise, proceed to Step 6. Step 5 ,therefore ,according to With R, r, , The functional relationship yields inequality 2. Solving inequality 2 gives the second range of values ​​for r, where... This is the minimum value of the grinding wheel's median diameter; Select the design radius of the end face arc of the grinding wheel head. The design radius of the arc at the end face of the grinding wheel head It falls within the second value range and satisfies the condition r ≥ 0.5D; Then select the design value for the grinding wheel diameter. ; Select the design value for the grinding wheel head thickness. ,satisfy and conditions; Step 6: Since r < 0.5D, D ≤ Therefore, r < ,according to With R, r, t, , The functional relationship is used to obtain inequality 3, and solving inequality 3 yields the third range of values ​​for r. Select the design radius of the end face arc of the grinding wheel head. The design radius of the arc at the end face of the grinding wheel head It falls within the range of the third value and satisfies ; Then select the design value for the grinding wheel diameter. ; In this step, select and satisfy +R≥0.5 conditions; Select the design value for the grinding wheel head thickness. ,satisfy and conditions; Select the design value of the grinding wheel diameter in step five. The method is as follows: based on the design radius of the arc of the grinding wheel head end face. Calculate the minimum value of the grinding wheel diameter. and the maximum value of the grinding wheel diameter At the minimum diameter of the grinding wheel With the maximum value of the grinding wheel diameter Choose the design value of the grinding wheel diameter. Design value of grinding wheel diameter Need to meet ; Select the design value of the grinding wheel diameter in steps three and six. The method is as follows: based on the design radius of the arc of the grinding wheel head end face. Calculate the minimum value of the grinding wheel diameter. and the maximum value of the grinding wheel diameter At the minimum diameter of the grinding wheel With the maximum value of the grinding wheel diameter Choose the design value of the grinding wheel diameter. Design value of grinding wheel diameter Need to meet ; Inequality 1 is as follows: ； Inequality 2 is as follows: ； Inequality 3 is as follows: ； 。 2. The design method of a milling wheel and elastic clamp according to claim 1, characterized in that, With R, r, t, , The functional relationship is: 。 3. The design method of a milling wheel and elastic clamp according to claim 2, characterized in that, calculate The formula is: 。 4. The design method of a milling wheel and elastic clamp according to claim 3, characterized in that, The maximum groove depth is related to R, r, t, The relationship between D and D is: 。 5. The design method of a milling wheel and elastic clamp according to claim 4, characterized in that, When the grinding wheel obtained according to the design method is used to mill optical parts, the spherical surface of the grinding wheel head is tangent to the glass spherical surface of the optical part being processed. At this time, the thickness h of the grinding wheel head satisfies the constraint condition h≥2rsinα.

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