Helical line discretization method, apparatus, device, and computer readable storage medium

Abstract

The application discloses a helix discrete method, device, equipment and computer readable storage medium, and belongs to the technical field of ultra-precision machining. The application obtains the feed speed of a tool, the rotation radius of a workpiece, and preset variable-chord-length discrete parameters, wherein the variable-chord-length discrete parameters are used for variable-chord-length discretization of a target helix, and the target helix is a turning track of slow-tool servo turning; the total arc length of the target helix is calculated according to the feed speed and the rotation radius; the target helix is subjected to variable-chord-length discretization according to the variable-chord-length discrete parameters and the total arc length of the target helix, so that the radial distance and the rotation angle of discrete points on the target helix are obtained. The application solves the technical problem that the discrete points generated by a traditional discrete algorithm are distributed unreasonably, and the precision of a workpiece surface is reduced when a slow-tool servo turning machine processes a free curved surface, and the machining precision of the slow-tool servo turning machine when processing the free curved surface on the workpiece surface is improved.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision machining technology, and in particular to a method, apparatus, device, and computer-readable storage medium for discretizing helical lines. Background Technology

[0002] Slow-speed servo turning is a commonly used ultra-precision cutting method suitable for machining free-form surfaces. Since the turning trajectory in slow-speed servo turning is usually an equidistant helix, a discretization algorithm is generally used to discretize the equidistant helix when planning the toolpath.

[0003] In related technologies, the discrete points obtained by the equal angle discretization algorithm are distributed radially from the center, resulting in severe redundancy in the central region of the workpiece. Furthermore, radial machining patterns are prone to appear on the workpiece surface, affecting the surface accuracy of the workpiece. In contrast, the discrete points obtained by the equal arc length discretization algorithm are fewer in number and evenly distributed on the workpiece surface, resulting in higher surface accuracy. However, the discrete points in the central region of the workpiece are sparsely distributed, leading to lower surface accuracy in the central region of the workpiece. Summary of the Invention

[0004] The main objective of this invention is to provide a helical discretization method, apparatus, device, and computer-readable storage medium, aiming to solve the technical problem that the distribution of discrete points generated by traditional discretization algorithms is unreasonable, resulting in low workpiece surface accuracy when machining free-form surfaces using slow-tool servo turning.

[0005] To achieve the above objectives, the present invention provides a helical discretization method, which is applied to slow-tool servo turning. The method includes:

[0006] The tool feed rate, workpiece rotation radius, and preset variable arc length discrete parameters are obtained. The variable arc length discrete parameters are used to perform variable arc length discretization on the target helix, and the target helix is ​​the turning trajectory of the slow tool servo turning.

[0007] The total arc length of the target helix is ​​calculated based on the feed rate and the radius of rotation.

[0008] Based on the variable arc length discretization parameter and the total arc length of the target spiral, the target spiral is discretized by variable arc length to obtain the radial distance and rotation angle of the discrete points on the target spiral.

[0009] Optionally, the step of calculating the total arc length of the target helix based on the feed rate and the radius of rotation includes:

[0010] The total number of turns of the target helix is ​​calculated based on the feed rate and the radius of rotation.

[0011] The total rotation angle of the target helix is ​​determined based on the total number of turns of the target helix.

[0012] The total arc length of the target helix is ​​calculated based on the total rotation angle of the target helix and the feed rate.

[0013] Optionally, the step of performing variable arc length discretization on the target spiral based on the variable arc length discretization parameter and the total arc length of the target spiral to obtain the radial distance and rotation angle of discrete points on the target spiral includes:

[0014] Based on the variable arc length discrete parameters and the total arc length of the target spiral, the total arc length of each discrete point on the target spiral is determined, wherein the total arc length of the discrete point is the arc length between the discrete point and the center of the workpiece.

[0015] The rotation angle of each discrete point is calculated based on the total arc length of each discrete point and the feed rate.

[0016] The radial distance of each discrete point is calculated based on the rotation angle of each discrete point and the feed rate.

[0017] Optionally, the variable arc length discrete parameter includes an arc length leading term and an arc length tolerance. The step of determining the total arc length of each discrete point on the target spiral based on the variable arc length discrete parameter and the total arc length of the target spiral includes:

[0018] The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the arc length tolerance, and the total arc length of the target spiral.

[0019] Optionally, the variable arc length discrete parameter includes the arc length first term and the arc length common ratio. The step of determining the total arc length of each discrete point on the target spiral based on the variable arc length discrete parameter and the total arc length of the target spiral includes:

[0020] The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the common ratio of the arc length, and the total arc length of the target spiral.

[0021] Optionally, the step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes:

[0022] The rotation angle of each discrete point is calculated using the circular arc formula method based on the total arc length of each discrete point and the feed rate.

[0023] Optionally, the step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes:

[0024] The rotation angle of each discrete point is calculated using Newton's iteration method based on the total arc length of each discrete point and the feed rate.

[0025] Furthermore, to achieve the above objectives, the present invention also provides a helical discretization device, which is applied to slow-tool servo turning, the device comprising:

[0026] The parameter acquisition module is used to acquire the tool feed rate, the workpiece rotation radius, and the preset variable arc length discrete parameters. The variable arc length discrete parameters are used to perform variable arc length discretization on the target helix, and the target helix is ​​the turning trajectory of the slow tool servo turning.

[0027] The helix discretization module is used to calculate the total arc length of the target helix based on the feed speed and the radius of rotation; and to perform variable arc length discretization on the target helix based on the variable arc length discretization parameters and the total arc length of the target helix to obtain the radial distance and rotation angle of the discrete points on the target helix.

[0028] Furthermore, to achieve the above objectives, the present invention also provides a helical discretization device, the device comprising: a memory, a processor, and a helical discretization program stored in the memory and executable on the processor, the helical discretization program being configured to implement the steps of the helical discretization method as described above.

[0029] In addition, to achieve the above objectives, the present invention also provides a computer-readable storage medium storing a spiral discretization program, which, when executed by a processor, implements the steps of the spiral discretization method as described above.

[0030] This invention proposes a variable arc length discretization algorithm, which can perform regular discretization processing on a continuous spiral according to a preset arc length variation law. It obtains the tool feed rate, workpiece rotation radius, and preset variable arc length discretization parameters, where the variable arc length discretization parameters are used to discretize the target spiral, which is the turning trajectory of a slow-tool servo turning process. The algorithm calculates the total arc length of the target spiral based on the feed rate and rotation radius. Then, it performs variable arc length discretization on the target spiral based on the variable arc length discretization parameters and the total arc length of the target spiral, obtaining the radial distance and rotation angle of the discrete points on the target spiral. This variable arc length discretization controls the arc length of the discrete points on the target spiral to vary according to the preset arc length. The variation of the discrete point distribution along the target spiral is made more reasonable, thus solving the technical problem of unreasonable discrete point distribution generated by traditional discrete algorithms, which leads to reduced workpiece surface accuracy when machining free-form surfaces with slow-tool servo turning. For example, the discrete point distribution in the center region of the workpiece is too dense in the equal-radius discrete algorithm, which can easily lead to overcutting in the center region and undercutting at the edge region when cutting the workpiece based on the discrete points generated by the equal-angle discrete algorithm. On the other hand, the discrete point distribution in the center region of the workpiece is too sparse in the equal-arc length discrete algorithm, which can easily lead to large deviations in the accuracy of slow-tool servo turning in the center region of the workpiece where the curvature changes drastically when cutting the workpiece based on the discrete points generated by the equal-radius discrete algorithm. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the first embodiment of the spiral discretization method of the present invention;

[0032] Figure 2 This is a schematic diagram illustrating the calculation process of the total arc length of the spiral in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of the variable arc length discretization process according to an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the helical discretization device involved in the embodiments of the present invention;

[0035] Figure 5 This is a schematic diagram of the structure of a spiral discrete device in the hardware operating environment involved in the embodiments of the present invention.

[0036] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0037] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0038] This invention provides a method for discretizing helical lines, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the spiral discretization method of the present invention.

[0039] In this embodiment, the helical discretization method is applied to slow-tool servo turning, and the method includes:

[0040] Step S100: Obtain the tool feed rate, the workpiece rotation radius, and the preset variable arc length discrete parameters, wherein the variable arc length discrete parameters are used to perform variable arc length discretization on the target helix, and the target helix is ​​the turning trajectory of the slow tool servo turning.

[0041] Slow Tool Servo (STS) is a precision machining technology primarily used for machining complex curved surfaces, especially free-form surfaces. It is commonly found in the manufacturing of optical components, precision mechanical parts, and other applications requiring extremely high-precision contours. The core feature of this technology is the transformation of the traditional lathe spindle into a C-axis whose position and speed can be precisely controlled. This allows the lathe to achieve simultaneous movement along the X, Z, and C axes, creating complex motions within a cylindrical coordinate system.

[0042] During slow-speed servo turning, the machine tool's control system performs highly coordinated motion control of the spindle and tool according to a pre-planned toolpath and tool compensation strategy. Typically, the spindle (C-axis) rotates at a certain speed and in a certain direction, while the Z-axis and X-axis reciprocate synchronously along precisely calculated sine or other complex trajectories. Multi-axis interpolation technology ensures the tool moves along a precise trajectory on the workpiece surface. Specifically, when the C-axis and X-axis perform interpolation motion simultaneously, the X-axis tool feeds linearly from the workpiece center to the workpiece edge at a constant feed rate, while the workpiece rotates clockwise or counterclockwise under the influence of the C-axis. The combined trajectory of these two movements (i.e., the turning trajectory in this embodiment) is an equidistant helix.

[0043] Those skilled in the art will understand that in order to machine a workpiece into a specified surface shape, a mathematical model needs to be established based on that specified surface shape. This mathematical model is then projected onto the plane corresponding to the X-axis and C-axis to obtain the cutting trajectory of the tool on this plane, which is the target helix in this embodiment. In other words, the target helix is ​​known before machining the workpiece. After determining the target helix, in order to accurately control the cutting process and achieve complex contour machining, it is generally necessary to discretize the cutting trajectory (i.e., the target helix) of slow-tool servo turning, decomposing it into a series of discrete points or small segments of continuous linear or circular interpolation motions that the CNC machine tool can understand and execute. This allows the CNC system to accurately control the synchronous movement of the X-axis and C-axis through interpolation algorithms, ensuring that the tool can cut according to the designed shape and precision requirements, thereby improving machining accuracy.

[0044] When discretizing the target helix, traditional discretization algorithms include equal-angle discretization and equal-radius discretization. However, when cutting the workpiece using discrete points generated by the equal-angle discretization algorithm, overcutting easily occurs in the workpiece's central region, while undercutting easily occurs at the workpiece's edges. Conversely, the equal-radius discretization algorithm results in a sparse distribution of discrete points in the workpiece's central region, leading to significant deviations in the accuracy of slow-tool servo turning in the workpiece's central region where curvature changes drastically. This unreasonable distribution of discrete points generated by traditional discretization algorithms results in low workpiece surface accuracy during slow-tool servo turning of free-form surfaces. Therefore, this embodiment proposes a variable-radius-length helix discretization method. By pre-setting variable-radius-length discretization parameters before formal machining, the distribution of discrete points on the target helix (i.e., the distribution of tool contact points on the workpiece surface) becomes more reasonable and uniform, thereby precisely controlling the cutting process and ensuring that the tool can cut according to the designed shape and accuracy requirements, resulting in a free-form surface with excellent surface quality and extremely high surface accuracy.

[0045] In this embodiment, the turning trajectory of slow-tool servo turning refers to the composite trajectory when the C-axis and X-axis simultaneously perform interpolation movements. This composite trajectory is generally an equidistant helix. It is easy to understand that the workpiece is fixed on the C-axis, with its center connected to the C-axis. The workpiece rotates around its center, while the tool, under the control of the X-axis, feeds from the tool center towards the workpiece edge, cutting on the workpiece surface. In actual slow-tool servo turning, the tool also performs turning at different depths on the workpiece surface under the control of the Z-axis. This embodiment does not consider the cutting motion in the Z-axis direction; it only discretizes the composite trajectory of the synchronous movement of the X-axis and C-axis by varying the arc length, thereby determining the contact point (i.e., the discrete point) between the tool and the workpiece surface on this composite trajectory (i.e., the target helix). After determining the contact point between the tool and the workpiece surface on the composite trajectory, the tool's movement on the Z-axis can be synchronized through certain algorithm calculations. Finally, a tool path that the CNC machine tool can understand and execute is generated. Thus, through multi-axis joint motion, the tool is controlled to perform high-precision cutting on the workpiece according to the tool path, and the specified surface shape will be cut on the workpiece.

[0046] It should be noted that the diameter of gyration refers to the diameter of the largest circle projected by the trajectory of an object moving in a circle around an axis. Correspondingly, the radius of gyration refers to the radius of the largest circle projected by the trajectory of an object moving in a circle around an axis. In this embodiment, the workpiece center is connected to the C-axis. With the workpiece center as the center, the C-axis drives the workpiece to rotate in a circular motion. Under the control of the X-axis, the tool cuts the workpiece surface at a certain feed rate, thereby forming an equidistant helical turning trajectory on the workpiece surface, which is the target helical line in this embodiment. Therefore, the radius of gyration of the workpiece in this embodiment refers to the maximum radial distance of the target helical line on the workpiece surface when the target helical line is projected onto the workpiece surface with the workpiece center as the starting point (i.e., the center point of the target helical line), which is also the radial distance of the point where the target helical line intersects the workpiece edge.

[0047] Step S200: Calculate the total arc length of the target spiral based on the feed rate and the radius of rotation;

[0048] In this embodiment, the target helix is ​​an equidistant helix (i.e., an Archimedean helix). Based on the relationship between radial distance, rotation angle, and feed rate, the helix equation of the target helix is ​​obtained as follows:

[0049]

[0050] Where ρ is the radial distance, usually in millimeters, f is the feed rate, usually in millimeters per revolution, and θ is the rotation angle, usually in radians.

[0051] The formula for calculating the arc length of an equidistant spiral is as follows:

[0052]

[0053] Where L is the arc length, f is the feed rate, and θ is the rotation angle.

[0054] Specifically, please refer to Figure 2 , Figure 2 This is a schematic diagram of the calculation process for the total arc length of the helix according to an embodiment of the present invention. Step S200 includes:

[0055] Step S210: Calculate the total number of turns of the target spiral based on the feed rate and the radius of rotation;

[0056] In this embodiment, assuming the radius of rotation is R (mm) and the feed rate is f (mm per revolution), the total number of turns of the target helix is ​​N = R / f (turns).

[0057] Step S220: Determine the total rotation angle of the target spiral based on the total number of turns of the target spiral;

[0058] In this embodiment, if the total number of turns of the target helix is ​​N (turns), then the total rotation angle θ of the target helix is... sum = 2π*N (radians).

[0059] Step S230: Calculate the total arc length of the target spiral based on the total rotation angle of the target spiral and the feed speed.

[0060] In this embodiment, if the total rotation angle of the target helix is ​​calculated to be θ sum Given the total rotation angle (radians) and the tool feed rate f (millimeters per revolution), substituting this total rotation angle and feed rate into the above formula for calculating the arc length of an equidistant helix, the total arc length L of the target helix can be obtained. sum (millimeters).

[0061] Step S300: Based on the variable arc length discretization parameter and the total arc length of the target spiral, perform variable arc length discretization on the target spiral to obtain the radial distance and rotation angle of the discrete points on the target spiral.

[0062] In this embodiment, different variable arc length discretization parameters can be input to perform corresponding variable arc length discretization on the target helix according to the user's needs.

[0063] In one example, the user wants to discretize the target spiral with arithmetic progression and variable arc length (i.e., discretize with arc length varying arithmetic progression). The user can input the corresponding tolerance and first term as the variable arc length discretization parameters.

[0064] In another example, the user wants to discretize the target spiral with equal-ratio side arc lengths (i.e., discretize with arc lengths varying proportionally). The user can input the corresponding common ratio and first term as the variable arc length discretization parameters.

[0065] It is not difficult to understand that, in addition to arithmetic and geometric progressions, other progressions such as exponential progressions can also be set, and appropriate parameters can be set accordingly as discrete parameters for variable arc length.

[0066] This embodiment provides a variable arc length discretization algorithm. This algorithm can perform regular discretization of a continuous spiral according to a preset arc length variation law. It obtains the tool feed rate, workpiece rotation radius, and preset variable arc length discretization parameters. The variable arc length discretization parameters are used to discretize the target spiral, which is the turning trajectory of a slow-tool servo turning process. The algorithm calculates the total arc length of the target spiral based on the feed rate and rotation radius. Then, it discretizes the target spiral according to the variable arc length discretization parameters and the total arc length of the target spiral, obtaining the radial distance and rotation angle of the discrete points on the target spiral. This variable arc length discretization controls the arc length of the discrete points on the target spiral to vary according to the preset arc length variation law, thus ensuring that the discrete points... The distribution along the target spiral is more reasonable, improving the machining accuracy of slow-tool servo turning when machining free-form surfaces on workpieces. It solves the technical problem that the unreasonable distribution of discrete points generated by traditional discrete algorithms leads to a decrease in the surface accuracy of workpieces when machining free-form surfaces using slow-tool servo turning. For example, the distribution of discrete points in the central region of the workpiece is too dense in the equal-arc discrete algorithm, which can easily lead to overcutting in the central region of the workpiece and undercutting in the edge region when cutting the workpiece based on the discrete points generated by the equal-angle discrete algorithm. On the other hand, the distribution of discrete points in the central region of the workpiece is too sparse in the equal-arc discrete algorithm, which can easily lead to a large deviation in the accuracy of slow-tool servo turning in the central region of the workpiece where the curvature changes drastically when cutting the workpiece based on the discrete points generated by the equal-arc discrete algorithm.

[0067] In one possible implementation, please specify the parameters. Figure 3 , Figure 3 This is a schematic diagram of the variable arc length discretization process according to an embodiment of the present invention. The step of performing variable arc length discretization on the target spiral based on the variable arc length discretization parameters and the total arc length of the target spiral to obtain the radial distance and rotation angle of the discrete points on the target spiral includes:

[0068] Step S310: Determine the total arc length of each discrete point on the target spiral line according to the variable arc length discrete parameter and the total arc length of the target spiral line, wherein the total arc length of the discrete point is the arc length between the discrete point and the center of the workpiece;

[0069] In this embodiment, according to user requirements, the target spiral can be discretized using arithmetic progression with varying arc lengths. Specifically, the varying arc length discretization parameters include the arc length first term and the arc length tolerance. The step of determining the total arc length of each discrete point on the target spiral based on the varying arc length discretization parameters and the total arc length of the target spiral includes:

[0070] Step S311: Calculate the total arc length of each discrete point on the target spiral line based on the first term of the arc length, the arc length tolerance, and the total arc length of the target spiral line.

[0071] Those skilled in the art will know that during slow-speed servo turning, the tool begins cutting from the tool center, which is also the center point of the target helix. The next tool contact point after the starting point is taken as the first discrete point, and the arc length of the first discrete point is the length of the arc on the target helix from the starting point to the first discrete point. The next tool contact point after the first discrete point is taken as the second discrete point, and the arc length of the second discrete point is the length of the arc on the target helix from the first discrete point to the second discrete point. This process continues until the last discrete point on the target helix.

[0072] It is easy to understand that in this embodiment, the first term of the arc length refers to the arc length of the first discrete point on the target spiral, and the arc length tolerance refers to the difference in arc lengths between any two adjacent discrete points on the target spiral. Based on the user-preset arc length tolerance and the first term of the arc length, an arithmetic sequence about arc lengths can be established, the sum of which is less than or equal to the total arc length of the target spiral. Using the relevant knowledge of arithmetic sequences, the number of discrete points on the target spiral and the arc length of each discrete point can be calculated, and thus the total arc length of each discrete point can be obtained. It should be specifically noted that the total arc length of the discrete points refers to the length of the arc between the center point of the target spiral and that discrete point.

[0073] To aid understanding, in one example, on a target spiral with arithmetic progression and varying arc lengths, discrete points A, B, and C are arranged sequentially from the starting point (i.e., the center point) to the ending point. The arc length of discrete point A is 1, the arc length of discrete point B is 2, and the arc length of discrete point C is 3. Therefore, the total arc length of discrete point A is 1, the total arc length of discrete point B is 3, and the arc length of discrete point C is 6.

[0074] This embodiment uses preset arc length first term and arc length tolerance as variable arc length discretization parameters to determine the arithmetic variation law of arc length, and performs arithmetic variable arc length discretization on the target spiral, so that the distribution of discrete points is more balanced and reasonable, thereby improving the surface machining accuracy of slow tool servo turning.

[0075] It is worth mentioning that the first and last terms of arc length can also be preset as variable arc length discretization parameters to perform arithmetic variable arc length discretization on the target spiral.

[0076] Furthermore, in addition to performing arithmetic-variable arc length discretization on the target spiral, geometric-variable arc length discretization can also be performed on the target spiral according to user requirements. Specifically, the variable arc length discretization parameters include the first term of the arc length and the common ratio of the arc lengths. The step of determining the total arc length of each discrete point on the target spiral based on the variable arc length discretization parameters and the total arc length of the target spiral includes:

[0077] Step S312: Calculate the total arc length of each discrete point on the target spiral line based on the first term of the arc length, the common ratio of the arc length, and the total arc length of the target spiral line.

[0078] In this embodiment, the common arc length ratio refers to the ratio of the arc lengths of any two adjacent discrete points on the target spiral. Based on the user-preset common arc length ratio and the first term of the arc length, a geometric sequence about the arc length can be established, the sum of which is less than or equal to the total arc length of the target spiral. Using the relevant knowledge of geometric sequences, the number of discrete points on the target spiral and the arc length of each discrete point can be calculated, and then the total arc length of each discrete point can be obtained.

[0079] This embodiment uses preset arc length first term and arc length common ratio as variable arc length discretization parameters to determine the proportional change law of arc length, and performs proportional variable arc length discretization on the target spiral, so that the distribution of discrete points is more balanced and reasonable, thereby improving the surface machining accuracy of slow tool servo turning.

[0080] It is worth mentioning that the first and last terms of arc length can also be preset as variable arc length discretization parameters to perform proportional variable arc length discretization on the target spiral.

[0081] In addition to arithmetic and geometric arc length variation patterns, exponential arc length variation patterns can also be set.

[0082] Step S320: Calculate the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate;

[0083] In this embodiment, after determining the total arc length of each discrete point, the rotation angle of each discrete point can be calculated by reverse calculation using the above arc length calculation formula.

[0084] Step S330: Calculate the radial distance of each discrete point based on the rotation angle of each discrete point and the feed speed.

[0085] In this embodiment, after determining the rotation angle of each discrete point, the rotation angle and feed rate of each discrete point can be substituted into the above helical equation in sequence, and the radial distance of each discrete point can be obtained by solving.

[0086] This embodiment uses preset variable arc length discretization parameters to perform corresponding variable arc length discretization on the target helix (e.g., arithmetic variable arc length discretization, geometric variable arc length discretization, exponential variable arc length discretization, etc.). Then, it uses relevant mathematical knowledge (e.g., arithmetic sequence knowledge related to arithmetic variable arc length discretization) to calculate the total arc length of each discrete point. Finally, it uses the arc length calculation formula and helix equation of the equidistant helix to calculate the radial distance and rotation angle of each discrete point, thereby achieving a reasonable distribution of discrete points and improving the machining accuracy of slow tool servo turning when machining free-form surfaces on the workpiece surface.

[0087] Further, in one possible implementation, the step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes:

[0088] Step S321: Calculate the rotation angle of each discrete point using the circular arc formula method based on the total arc length of each discrete point and the feed rate.

[0089] In this embodiment, since the equation for calculating the rotation angle using the arc length calculation formula is extremely complex and difficult to calculate directly, the circular arc formula method can be used to approximate the radial distance and rotation angle of each discrete point. Those skilled in the art will know that the circular arc formula method approximates the arc between two adjacent discrete points as a circular arc, and uses the arc length calculation formula (radius multiplied by radians equals arc length) to approximately solve for the radial distance and rotation angle of each discrete point of the helix. Those skilled in the art have already conducted in-depth research on this method, and this embodiment will not elaborate further.

[0090] Further, the step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes:

[0091] Step S322: Based on the total arc length of each discrete point and the feed rate, calculate the rotation angle of each discrete point using the Newton-Raphson iteration method.

[0092] In this embodiment, the equation for calculating the rotation angle using the arc length formula is extremely complex and difficult to calculate directly. Furthermore, the theoretical error of the circular arc formula approximation increases as the radial path of the discrete point decreases; the closer the discrete point is to the workpiece center, the greater the error obtained by the circular arc formula approximation. Therefore, this embodiment proposes using the Newton-Raphson iteration method to improve the calculation accuracy of the radial distance and rotation angle of the discrete point, reduce the error, and thus obtain a more accurate discrete point position, thereby improving the machining accuracy of slow-tool servo turning. The Newton-Raphson iteration method is a commonly used mathematical calculation method that approximates the solution of equations in the real and complex number domains. This embodiment will not elaborate further on it.

[0093] In addition, the present invention also provides a spiral discretization device, please refer to Figure 4 , Figure 4 This is a schematic diagram of a spiral discretization device according to an embodiment of the present invention. The device includes:

[0094] The parameter acquisition module 10 is used to acquire the feed rate of the tool, the turning radius of the workpiece, and the preset variable arc length discrete parameters. The variable arc length discrete parameters are used to perform variable arc length discretization on the target helix, and the target helix is ​​a slow tool servo turning trajectory.

[0095] The helix discretization module 20 is used to calculate the total arc length of the target helix based on the feed speed and the radius of rotation; and to perform variable arc length discretization on the target helix based on the variable arc length discretization parameters and the total arc length of the target helix to obtain the radial distance and rotation angle of the discrete points on the target helix.

[0096] In one embodiment, the helical discretization module 20 is further configured to:

[0097] The total number of turns of the target helix is ​​calculated based on the feed rate and the radius of rotation.

[0098] The total rotation angle of the target helix is ​​determined based on the total number of turns of the target helix.

[0099] The total arc length of the target helix is ​​calculated based on the total rotation angle of the target helix and the feed rate.

[0100] In one embodiment, the helical discretization module 20 is further configured to:

[0101] Based on the variable arc length discrete parameters and the total arc length of the target spiral, the total arc length of each discrete point on the target spiral is determined, wherein the total arc length of the discrete point is the arc length between the discrete point and the center of the workpiece.

[0102] The rotation angle of each discrete point is calculated based on the total arc length of each discrete point and the feed rate.

[0103] The radial distance of each discrete point is calculated based on the rotation angle of each discrete point and the feed rate.

[0104] In one embodiment, the variable arc length discrete parameters include the arc length first term and the arc length tolerance. The helical discrete module 20 is further used for:

[0105] The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the arc length tolerance, and the total arc length of the target spiral.

[0106] In one embodiment, the variable arc length discrete parameters include the arc length first term and the arc length common ratio. The helical discrete module 20 is further used for:

[0107] The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the common ratio of the arc length, and the total arc length of the target spiral.

[0108] In one embodiment, the helical discretization module 20 is further configured to:

[0109] The rotation angle of each discrete point is calculated using the circular arc formula method based on the total arc length of each discrete point and the feed rate.

[0110] In one embodiment, the helical discretization module 20 is further configured to:

[0111] The rotation angle of each discrete point is calculated using Newton's iteration method based on the total arc length of each discrete point and the feed rate.

[0112] The helical discretization device provided in this invention, employing the helical discretization method described in the above embodiments, can solve the technical problem of low workpiece surface accuracy during slow-tool servo turning due to the unreasonable distribution of discrete points generated by traditional discretization algorithms. Compared with the prior art, the beneficial effects of the helical discretization device provided in this invention are the same as those of the helical discretization method provided in the above embodiments, and other technical features in the helical discretization device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0113] Furthermore, the present invention also provides a helical discretization device, which includes a memory, a processor, and a helical discretization program stored in the memory and executable on the processor. When the helical discretization program is executed by the processor, it implements the steps of the helical discretization method as described above.

[0114] Please refer to Figure 5 , Figure 5 This is a schematic diagram of the structure of a spiral discrete device in the hardware operating environment involved in the embodiments of the present invention.

[0115] like Figure 5As shown, the spiral discrete device may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed random access memory (RAM) or a stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0116] Those skilled in the art will understand that Figure 5 The structure shown does not constitute a limitation on the discrete spiral device and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0117] like Figure 5 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and a spiral discrete program.

[0118] exist Figure 5 In the spiral discretization device shown, the network interface 1004 is mainly used for data communication with other devices; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and the memory 1005 in the spiral discretization device of the present invention can be set in the spiral discretization device, and the spiral discretization device calls the spiral discretization program stored in the memory 1005 through the processor 1001 and executes the spiral discretization method provided in the embodiment of the present invention.

[0119] Furthermore, the present invention also provides a computer-readable storage medium storing a spiral discretization program, which, when executed by a processor, implements the steps of the spiral discretization method as described above.

[0120] The specific implementation of the computer-readable storage medium of the present invention is basically the same as the embodiments of the spiral discretization method described above, and will not be repeated here.

[0121] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0122] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0123] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0124] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for discretizing helical lines, characterized in that, The spiral discretization method is applied to slow-tool servo turning, and the method includes the following steps: The tool feed rate, workpiece rotation radius, and preset variable arc length discretization parameters are obtained. The variable arc length discretization parameters are used to discretize the target helix, which is the turning trajectory of the slow tool servo turning. The variable arc length discretization parameters are either arithmetic variable arc length discretization parameters or geometric variable arc length discretization parameters. The arithmetic variable arc length discretization parameters are used to discretize the target helix using arithmetic variable arc length discretization, and the geometric variable arc length discretization parameters are used to discretize the target helix using geometric variable arc length discretization. The total arc length of the target helix is ​​calculated based on the feed rate and the radius of rotation. Based on the variable arc length discretization parameter and the total arc length of the target spiral, the target spiral is discretized by variable arc length to obtain the radial distance and rotation angle of the discrete points on the target spiral.

2. The spiral discretization method as described in claim 1, characterized in that, The step of calculating the total arc length of the target helix based on the feed rate and the radius of rotation includes: The total number of turns of the target helix is ​​calculated based on the feed rate and the radius of rotation. The total rotation angle of the target helix is ​​determined based on the total number of turns of the target helix. The total arc length of the target helix is ​​calculated based on the total rotation angle of the target helix and the feed rate.

3. The spiral discretization method as described in claim 2, characterized in that, The step of discretizing the target spiral with varying arc length based on the varying arc length discretization parameters and the total arc length of the target spiral to obtain the radial distance and rotation angle of discrete points on the target spiral includes: Based on the variable arc length discrete parameters and the total arc length of the target spiral, the total arc length of each discrete point on the target spiral is determined, wherein the total arc length of the discrete point is the arc length between the discrete point and the center of the workpiece. The rotation angle of each discrete point is calculated based on the total arc length of each discrete point and the feed rate. The radial distance of each discrete point is calculated based on the rotation angle of each discrete point and the feed rate.

4. The spiral discretization method as described in claim 3, characterized in that, The variable arc length discrete parameter is an arithmetic variable arc length discrete parameter, which includes the arc length first term and the arc length tolerance. The step of determining the total arc length of each discrete point on the target spiral based on the variable arc length discrete parameter and the total arc length of the target spiral includes: The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the arc length tolerance, and the total arc length of the target spiral.

5. The spiral discretization method as described in claim 3, characterized in that, The variable arc length discrete parameter is a geometrically variable arc length discrete parameter, which includes the first term of the arc length and the common ratio of the arc length. The step of determining the total arc length of each discrete point on the target spiral based on the variable arc length discrete parameter and the total arc length of the target spiral includes: The total arc length of each discrete point on the target spiral is calculated based on the first term of the arc length, the common ratio of the arc length, and the total arc length of the target spiral.

6. The spiral discretization method as described in claim 4 or 5, characterized in that, The step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes: The rotation angle of each discrete point is calculated using the circular arc formula method based on the total arc length of each discrete point and the feed rate.

7. The spiral discretization method as described in claim 4 or 5, characterized in that, The step of calculating the rotation angle of each discrete point based on the total arc length of each discrete point and the feed rate includes: The rotation angle of each discrete point is calculated using Newton's iteration method based on the total arc length of each discrete point and the feed rate.

8. A spiral discretization device, characterized in that, The spiral discretization device is applied to slow-tool servo turning, and the device includes: The parameter acquisition module is used to acquire the tool feed rate, the workpiece rotation radius, and preset variable arc length discrete parameters. The variable arc length discrete parameters are used to perform variable arc length discretization on the target helix, which is the turning trajectory of the slow tool servo turning. The variable arc length discrete parameters are either arithmetic variable arc length discrete parameters or geometric variable arc length discrete parameters. The arithmetic variable arc length discrete parameters are used to perform arithmetic variable arc length discretization on the target helix, and the geometric variable arc length discrete parameters are used to perform geometric variable arc length discretization on the target helix. The helix discretization module is used to calculate the total arc length of the target helix based on the feed speed and the radius of rotation; and to perform variable arc length discretization on the target helix based on the variable arc length discretization parameters and the total arc length of the target helix to obtain the radial distance and rotation angle of the discrete points on the target helix.

9. A spiral discretization device, characterized in that, The device includes: a memory, a processor, and a spiral discretization program stored in the memory and executable on the processor, the spiral discretization program being configured to implement the steps of the spiral discretization method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a spiral discretization program, which, when executed by a processor, implements the steps of the spiral discretization method as described in any one of claims 1 to 7.

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