Method for determining path of diamond turning tool with large-gradient rotational symmetry surface shape

Abstract

The invention discloses a method for determining a path of a diamond turning tool with a large-gradient rotational symmetry surface shape. The method comprises the following steps of: firstly, dividing a curvilinear equation of a processing object into a series of discrete data points according to an equal arc length method or an equal interval method and the like; then, calculating unit normal vectors corresponding to the discrete points according to a curvilinear equation; and then, mapping the measured surface shape error to a curvilinear equation of a processed object according to a unit normal vector of a corresponding point, and finally, adding cutter radius compensation on a cutter path according to the unit normal vector of the corresponding point, and outputting a processing program according to a machine tool numerical control program format. According to the method for determining the path of the diamond turning tool, the number of times of surface shape compensation of single-point diamond turning can be reduced, the convergence speed is increased, particularly for a large-gradient surface shape, the surface shape convergence speed is higher than that of a conventional diamond turning tool, and the machining precision and the machining efficiency of the whole process are improved on the whole.

Description

Technical Field

[0001] This invention belongs to the field of optical freeform surface manufacturing technology, specifically relating to a method for determining the path of a diamond turning tool for steeply angular rotationally symmetrical surfaces. It is applicable to the machining of steeply angular spherical and aspherical surfaces, such as non-ferrous metals and infrared crystal materials. Background Technology

[0002] Infrared optical systems are a key technological support for my country's space optics, national defense, and military industries. They undertake high-resolution imaging and all-weather observation tasks in payloads such as remote sensing satellites and space telescopes, providing core effective payloads for major projects such as manned spaceflight, lunar exploration, and space broadband. In national defense, infrared imaging enables target detection and surveillance in complex environments such as day and night and fog and haze. It serves as the "eyes" for intelligence early warning, precision guidance, and night vision command, significantly improving combat effectiveness and reducing the risk of friendly fire. The research and development of infrared optical systems has formed a dual-use industrial chain, promoting the simultaneous progress of cutting-edge technologies such as high-end optical manufacturing, optoelectronic detection, and system integration, and supporting the modernization of national defense equipment and the development of high-end manufacturing.

[0003] However, the surface profile of optical elements in infrared optical systems is steeper than that of conventional visible light elements. The reasons are as follows:

[0004] (1) Improve numerical aperture (NA) and light flux - Infrared detectors have relatively low sensitivity, and systems often use large aperture and low F-number designs to collect more radiation energy, which requires lenses with greater optical power, i.e. steeper curvature.

[0005] (2) Limited material types and aspherical / freeform surface technology - The types of materials that can transmit light in the infrared band are limited. Traditional spherical lenses cannot meet the requirements of imaging quality and volume at the same time. Designers often use aspherical or freeform surface elements. These elements often have steeper local curvature to achieve higher-order aberration correction.

[0006] (3) Thermal sensitivity - The refractive index of high refractive index materials changes significantly with temperature, and temperature fluctuations can cause focal length drift. By using steeper curved surfaces and thermal compensation structures, the influence of thermal aberrations can be reduced to a certain extent.

[0007] For steep optical components, single-point diamond turning requires a larger tool radius, which significantly impacts the final surface accuracy of the component due to tool contour errors. In practice, it has also been found that single-point diamond turning of steep components using traditional DIFFSYS programming software (i.e., existing methods) results in low convergence rates, long processing times, and in severe cases, out-of-tolerance center thickness and component failure. Summary of the Invention

[0008] This invention addresses the shortcomings of existing machining methods, such as low convergence rate, numerous iterations (i.e., low convergence rate), and long machining cycles for machining steep-angle components. It proposes a method for determining the diamond turning tool trajectory for steep-angle, rotationally symmetric surfaces. This method reduces the number of surface compensation steps in single-point diamond turning, accelerates the convergence speed, and is particularly effective for steep-angle surfaces, achieving a faster convergence speed than conventional diamond turning tools. Overall, it improves the machining accuracy and efficiency of the entire process.

[0009] The technical solution adopted by this invention to solve its technical problem is:

[0010] A method for determining the path of a diamond turning tool with a steeply steep rotational symmetry plane, characterized by comprising the following steps:

[0011] S1. First, the curve equation of the object to be processed is divided into a series of discrete data points according to the equal arc length method or the equal spacing method.

[0012] S2. Calculate the unit normal vector corresponding to each discrete point based on the curve equation.

[0013] S3. Map the measured surface shape error onto the curve equation of the object being processed according to the unit normal vector of the corresponding point.

[0014] S4. Finally, according to the unit normal vector of the corresponding point, add tool radius compensation on the tool path, and output the machining program according to the machine tool CNC program format.

[0015] Furthermore, in step S1, based on the curve equation F of the object being processed, a sequence of n discrete points on curve F is established using either equal arc length or equal interval methods. (i=1,2,3…n);

[0016] The symbols are defined as follows:

[0017] = [ (i=1,2,3…n) is the sequence of original points on the curve;

[0018] = [ ] (i=1,2,3…n) is the sequence of X-axis coordinates on the curve.

[0019] Furthermore, in step S2, based on the curve equation F of the object being processed, combined with... = [ The equation of curve F is calculated using the formula (i=1,2,3…n). = [ The first derivative at (i=1,2,3…n) If (i=1,2,3…n), then define the curve equation F in = [ The unit normal vector at (i=1,2,3…n) is:

[0020] = [ (i=1,2,3…n)

[0021] Furthermore, in step S3, the program compensation amount is calculated based on the machining surface shape error. The specific method is as follows:

[0022] For the first processing, record ;

[0023] After the first (1+j)th compensation process (j = 1,2...m, m generally does not exceed 2), the original surface shape error data E output by the detection equipment is first obtained, combined with... = [ Interpolation (i=1,2,3…n) yields the error value at the corresponding point. Then the surface shape error corresponding to the (1+j)th iteration is:

[0024] = , , (j = 1,2...m)

[0025] The total error corresponding to the (1+j)th iteration is the sum of the errors at the corresponding points, denoted as...

[0026]

[0027] Furthermore, in step S3, the surface profile curve P with error compensation is calculated as follows:

[0028]

[0029] Note: Operator [ ] indicates that corresponding points of vectors are multiplied.

[0030] Furthermore, in step S4, if the radius of the diamond tool is denoted as R, then the tool trajectory profile with added tool radius compensation is... for

[0031]

[0032] Furthermore, in step S4, the tool path profile is determined according to the requirements of the machining equipment, such as the spindle rotation direction and turning direction. The output is a point sequence that conforms to the format requirements of CNC machine tool programs.

[0033] Furthermore, in step S4, if the processed surface shape is not qualified, the process returns to step (3).

[0034] Furthermore, in step S1, the equal arc length method refers to the fact that the arc lengths of two adjacent points on the curve equation F are approximately equal, that is...

[0035] , (i=1,2,3…n-2).

[0036] Furthermore, in step S1, the equal interval method refers to the fact that the X-axis coordinates of two adjacent points on the curve equation F are equally spaced, that is...

[0037] , (i=1,2,3…n-2).

[0038] Beneficial effects of the present invention

[0039] This invention discloses a method for determining the tool path in diamond turning of steeply slender, rotationally symmetric surfaces. Unlike traditional methods, which directly superimpose surface shape errors onto the tool path profile, this invention superimposes surface shape errors onto the tool profile according to the normal vectors of corresponding points. For relatively gentle surfaces, the difference between the two methods is minimal; however, for steeper surfaces, especially at the edges, the difference becomes significant. Traditional methods often result in severe "edge collapse" at the steepest edges, which cannot be converged even after multiple iterative compensation processes, ultimately leading to surface shape machining failure. The method described in this invention effectively suppresses this phenomenon. This invention significantly improves the surface shape convergence speed of single-point diamond turning, increases machining efficiency, and improves the overall machining efficiency of the entire process. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane as described in Specific Embodiment 1.

[0041] Figure 2 This is a schematic diagram of a steep aspherical surface example as described in Specific Embodiment 1;

[0042] Figure 3 This is a comparison diagram of the tool path in this specific embodiment 1 and the tool path of the traditional machining method;

[0043] Figure 4 for Figure 3 A magnified view of a portion of the image. Detailed Implementation

[0044] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0045] See Figure 1-4 Specific embodiment 1: This embodiment 1 provides a method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane, characterized by the following steps:

[0046] S1. First, the curve equation of the object being processed is divided into a series of discrete data points using methods such as equal arc length or equal interval. In step S1, based on the curve equation F of the object being processed, a sequence of n discrete points on curve F is established using methods such as equal arc length or equal interval. (i=1,2,3…n);

[0047] The symbols are defined as follows:

[0048] = [ (i=1,2,3…n) is the sequence of original points on the curve;

[0049] = [ ] (i=1,2,3…n) is the sequence of X-axis coordinates on the curve.

[0050] In step S1, the equal arc length method means that the arc lengths of two adjacent points on the curve equation F are approximately equal, that is...

[0051] , (i=1,2,3…n-2).

[0052] Alternatively, in step S1, the equal interval method refers to the fact that the X-axis coordinates of two adjacent points on the curve equation F are equally spaced, i.e.

[0053] , (i=1,2,3…n-2).

[0054] In this embodiment 1, with Figure 2 Taking the concave surface of the drawing as an example, Figure 2 The parameters of the equation to be processed are: vertex radius of curvature R = 47.317, quadratic coefficient K = 1.545, and diameter φ59.32mm. Calculations show that the edge steepness of this surface reaches 89.711°.

[0055] According to the curve equation F= of the object being processed Establish a sequence of n discrete points on curve F with an equal arc length l = 0.005 mm. (i=1,2,3…n).

[0056] S2. Calculate the unit normal vector corresponding to each discrete point based on the curve equation; in step S2, based on the curve equation F of the object being processed, combined with... = [ The equation of curve F is calculated using the formula (i=1,2,3…n). = [ The first derivative at (i=1,2,3…n) If (i=1,2,3…n), then define the curve equation F in = [ The unit normal vector at (i=1,2,3…n) is:

[0057] = [ (i=1,2,3…n)

[0058] S3. Map the measured surface shape error onto the curve equation of the workpiece according to the unit normal vector of the corresponding point; in step S3, calculate the program compensation amount based on the machining surface shape error. The specific method is as follows:

[0059] For the first processing, record ;

[0060] After the first (1+j)th compensation process (j = 1,2...m, m generally does not exceed 2), the original surface shape error data E output by the detection equipment is first obtained, combined with... = [ Interpolation (i=1,2,3…n) yields the error value at the corresponding point. Then the surface shape error corresponding to the (1+j)th iteration is:

[0061] = , , (j = 1,2...m)

[0062] The total error corresponding to the (1+j)th iteration is the sum of the errors at the corresponding points, denoted as...

[0063]

[0064] In this embodiment 1, the second compensation machining after the first machining corresponds to the surface shape error of the (1+j)th machining.

[0065] = , , (j = 1).

[0066] In step S3, the surface profile curve P with error compensation is calculated as follows:

[0067]

[0068] Note: Operator [ ] indicates that corresponding points of vectors are multiplied.

[0069] S4. Finally, according to the unit normal vector of the corresponding point, add tool radius compensation to the tool path, and output the machining program according to the machine tool CNC program format. In step S4, let the radius of the diamond tool be R, then the tool path contour with added tool radius compensation is... for

[0070]

[0071] In step S4, the tool path profile is determined according to the spindle rotation direction, turning direction, and other root requirements of the machining equipment. The output is a point sequence that conforms to the format requirements of CNC machine tool programs.

[0072] In step S4, if the surface shape is not qualified, return to step (3).

[0073] Figure 3 This is a comparison diagram of the tool path in this specific embodiment 1 and the tool path of the traditional machining method. The X-axis represents the radius information, and 0 represents the center of rotational symmetry. The Y-axis represents the sag of the aspherical surface, and the unit is mm.

[0074] from Figure 3 and Figure 4As can be seen, in steep areas, the tool path generated by the traditional method and the tool path generated by the method in Embodiment 1 begin to differ. The tool path generated by the traditional method is lower at the edge than the path generated by this invention. This means that if the tool path follows the traditional path, it will cut more material than the path generated by this invention, resulting in overcutting on the workpiece surface and causing a "collapsed edge" phenomenon in the machined surface. In addition, machining the surface using the traditional path often requires multiple cuts (e.g., four or five cuts), while machining the surface using the tool path generated by the method in Embodiment 1 often only requires one cut to achieve precise machining. This difference leads to an inconsistency in the convergence rate (i.e., convergence speed) of the two methods. Machining the surface using the tool path generated by the method in Embodiment 1 significantly improves the surface convergence speed of single-point diamond turning (i.e., higher convergence rate or faster convergence speed), avoiding multiple iterations as with the traditional path, improving machining efficiency, and overall improving the overall process efficiency and shortening the machining cycle.

Claims

1. A method for determining the trajectory of a diamond turning tool with a steeply steep rotational symmetry plane, characterized in that, Includes the following steps: S1. First, the curve equation of the object to be processed is divided into a series of discrete data points according to the equal arc length method or the equal spacing method. S2. Calculate the unit normal vector corresponding to each discrete point based on the curve equation. S3. Map the measured surface shape error onto the curve equation of the object being processed according to the unit normal vector of the corresponding point. S4. Finally, according to the unit normal vector of the corresponding point, add tool radius compensation on the tool path, and output the machining program according to the machine tool CNC program format.

2. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 1, characterized in that, In step S1, based on the curve equation F of the object being processed, a sequence of n discrete points on curve F is established using either equal arc length or equal interval methods. (i=1,2,3…n); The symbols are defined as follows: = [ (i=1,2,3…n) is the sequence of original points on the curve; = [ ] (i=1,2,3…n) is the sequence of X-axis coordinates on the curve.

3. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 2, characterized in that, In step S2, based on the curve equation F of the object being processed, combined with... = [ The equation of curve F is calculated using the formula (i=1,2,3…n). = [ The first derivative at (i=1,2,3…n) If (i=1,2,3…n), then define the curve equation F in = [ The unit normal vector at (i=1,2,3…n) is: = [ ] (i=1,2,3…n)。 4. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 3, characterized in that, In step S3, the program compensation amount is calculated based on the machining surface shape error. The specific method is as follows: For the first processing, record ; After the first (1+j)th compensation process (j = 1,2...m, m generally does not exceed 2), the original surface shape error data E output by the detection equipment is first obtained, combined with... = [ Interpolation (i=1,2,3…n) yields the error value at the corresponding point. Then the surface shape error corresponding to the (1+j)th iteration is: = , , (j = 1,2...m) The total error corresponding to the (1+j)th iteration is the sum of the errors at the corresponding points, denoted as... 。 5. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 4, characterized in that, In step S3, the surface profile curve P with error compensation is calculated as follows: Note: Operator [ ] indicates that corresponding points of vectors are multiplied.

6. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 5, characterized in that, In step S4, let the radius of the diamond tool be R, then the tool trajectory profile with added tool radius compensation is... for 。 7. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 6, characterized in that, In step S4, the tool path profile is determined according to the spindle rotation direction, turning direction, and other root requirements of the machining equipment. The output is a point sequence that conforms to the format requirements of CNC machine tool programs.

8. The method for determining the trajectory of a diamond turning tool with a large steep rotational symmetry plane according to claim 7, characterized in that, If the processed surface shape is not qualified in step S4, the process returns to step S3.

9. A method for determining the path of a diamond turning tool for a steeply sloping rotationally symmetric surface, as described in any one of claims 2 to 8, characterized in that... The equal arc length method described in step S1 refers to the fact that the arc lengths of two adjacent points on the curve equation F are approximately equal, that is... , (i=1,2,3…n-2)。 10. A method for determining the path of a diamond turning tool for a steeply sloping rotationally symmetric surface, as described in any one of claims 2 to 8, characterized in that... The equal interval method described in step S1 refers to the fact that the X-axis coordinates of two adjacent points on the curve equation F are equally spaced, that is... , (i=1,2,3…n-2)。

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