Trajectory planning method for laser shaping of forming grinding wheels

Abstract

The present invention discloses a trajectory planning method for laser shaping of a formed grinding wheel. The trajectory planning is based on the fact that the laser beam cannot remove the abrasive particles when the laser effective power density is less than the abrasive particle laser removal energy threshold. A theoretical model of the laser effective power density and the abrasive particle laser removal energy threshold is established to avoid the situation where the laser beam still walks empty along the shaping trajectory after being unable to remove the abrasive particles in the later stage of shaping, thereby improving the shaping efficiency. At the same time, in order to further improve the shaping accuracy, a multi-track scanning method is designed to improve the overlap rate of the laser spot and the overlap rate of the scanning trajectory line.

Description

Technical Field

[0001] The invention belongs to the technical field of grinding wheel dressing, and in particular relates to a laser shaping trajectory planning method for a forming grinding wheel. Background Art

[0002] It is an industry consensus that the key to grinding formed grinding wheels is dressing. Due to its complex cross-sectional profile, extremely high abrasive hardness, and high bond holding strength, it is very difficult to dress formed grinding wheels, especially super-hard abrasive formed grinding wheels. Laser dressing is particularly suitable for dressing formed grinding wheels with complex cross-sectional profiles due to its advantages of being indestructible, highly controllable, and non-contact. During shaping, the laser beam needs to repeatedly scan the grinding wheel material along the shaping trajectory. In the later stage of shaping, as the incident angle and defocus increase, the laser irradiation spot area continues to increase, and the effective power density continues to decrease. When it is lower than the laser removal energy threshold of the abrasive, the laser beam cannot remove the diamond abrasive, and the laser beam will go empty along the shaping trajectory without removing the diamond abrasive. Therefore, how to design the laser shaping trajectory directly determines the efficiency of the laser shaping grinding wheel. In addition, the laser shaping accuracy mainly depends on the point / line overlap rate of the laser scanning trajectory, but in many cases, it is limited by the influence of equipment parameters, and the actual point / line overlap rate of the laser scanning trajectory is low, resulting in low shaping accuracy. At present, there is an urgent need for a scientific planning method for the laser shaping trajectory of the forming grinding wheel to maximize the shaping efficiency and accuracy.

[0003] In view of this, the present invention is proposed. Summary of the invention

[0004] The purpose of the present invention is to propose a method for planning the trajectory of laser shaping of a formed grinding wheel, so as to solve the problem mentioned in the background technology that when the effective power density of the laser is lower than the energy threshold of abrasive laser removal, the laser beam cannot remove the material, resulting in the laser beam running empty along the shaping trajectory and the shaping efficiency being reduced.

[0005] To achieve the above object, the technical solution of the present invention comprises the following steps:

[0006] Step 1: Since the V-shaped grinding wheel shaping trajectory is symmetrical, it can be divided into left and right sides, and the laser shaping trajectory design is carried out taking the right half as an example;

[0007] Step 2, establish a theoretical model of laser effective power density and abrasive laser removal energy threshold to determine the initial trajectory length;

[0008] Step 3: To further improve the dressing efficiency, design the trajectory increment and plan its length;

[0009] Step 4, planning the remaining shaping trajectories until all laser shaping trajectories are planned;

[0010] Step 5, using a spectrometer to collect the intensity of diamond characteristic spectral lines to verify the rationality of the trajectory planning path;

[0011] Step 6, design laser multi-scanning trajectories to increase the laser spot overlap rate and the laser scanning trajectory line overlap rate.

[0012] Furthermore, in step 1, the laser shaping track length L can be expressed as:

[0013] L=L0+L1+L2+···+L n

[0014] Furthermore, in step 2, the initial trajectory length L0 is designed to depend on the laser effective power density I A The energy threshold E of laser removal of abrasive particles 阈值 .

[0015] Further, in step 2, assuming that the diameter of the ablation pit or the width of the groove formed on the abrasive surface is w, the laser energy density at the edge of the ablation pit or the edge of the groove is This is the minimum laser energy value to remove the abrasive material, that is, the laser removal energy threshold E of the abrasive 阈值 , which can be expressed as:

[0016]

[0017] In the formula, is the laser energy density at the center of the beam, which can be expressed as: e p is the single pulse energy. ω0 is the spot radius of the laser beam at the focus. w is the width of the ablation pit / groove. When w = 0, Equal to the laser energy density at the center of the beam

[0018] Furthermore, taking the logarithm of both sides of the above equation:

[0019]

[0020] Furthermore, a single-pass laser ablation experiment was performed on the surface of the grinding wheel block, and then the laser single pulse energy logarithm lne was fitted. p With w 2 The linear relationship between w and ablation threshold of abrasive material can be deduced by setting w=0.

[0021] Furthermore, in step 2, the laser effective power density I A It can be expressed as:

[0022] I A =I p ×A c

[0023] In the formula, I p is the laser irradiation power density, A c is the laser absorption rate.

[0024] Laser irradiation power density I p It can be expressed as:

[0025]

[0026] Where P avg is the average laser power, f is the pulse repetition frequency, τ is the pulse width, and Per is the ratio of the laser power irradiated on the grinding wheel surface to the power emitted by the laser.

[0027] Furthermore, for the V-shaped grinding wheel, the laser scanning trajectory equation in the XOY plane is:

[0028]

[0029] Where θ is the V-shaped grinding wheel tip angle, B is the grinding wheel width, and R0 is the grinding wheel edge radius.

[0030] Initial parallel to the upper surface of the grinding wheel (above the XOY plane) equation:

[0031]

[0032] Where R is the radius of the grinding wheel.

[0033] Fundamental mode Gaussian laser beam equation:

[0034]

[0035] Where ω0 is the spot radius of the laser beam at the focus. x0, y0, z0 are the coordinates of the laser focus, r is the spot radius of the laser beam at the coordinate Z, and λ is the wavelength.

[0036] The irradiation spot area of ​​the laser beam on the parallel grinding wheel is:

[0037]

[0038] Where R is the radius of the grinding wheel, D xy is the projection area of ​​the laser beam irradiated surface in the XOY plane. The integration domains of x and y are:

[0039]

[0040] The ratio of the laser power irradiated on the grinding wheel surface to the laser power emitted is:

[0041]

[0042] Furthermore, in the XOY plane, the cross-section profile equation of the grinding wheel axis is:

[0043] y=R,

[0044] The cross-section profile of the shaft rotates around the X-axis to obtain the surface equation of the grinding wheel:

[0045] z 2 =R 2 -y 2

[0046] make:

[0047] f(x,y,z)=-R 2 +y 2 +z 2

[0048] Normal vector of the grinding wheel surface at any point:

[0049]

[0050] The laser incident angle refers to the angle between the center line of the laser beam and the outer normal of the grinding wheel surface at the laser incident point. Take the upper surface of the forming grinding wheel (above the XOY plane) for analysis. Since the center line of the laser beam is parallel to the Z axis, its unit vector is Combined with the external normal vector n of the grinding wheel surface at the laser incident point, according to the space vector and The angle formula can be used to calculate the incident angle of the laser beam.

[0051]

[0052] In the formula, m x ,m y ,m z Represents the projection of the space vector m on the x-axis, y-axis, and z-axis, n x ,n y ,n z Represents the projection of the space vector n on the x-axis, y-axis, and z-axis

[0053] Laser absorption rate A c It can be expressed as:

[0054]

[0055] In the formula, i is the refractive index and k is the extinction coefficient

[0056] Furthermore, in step 2, the laser effective power density I is calculated point by point along the laser shaping trajectory. A and the abrasive laser removal energy threshold E 阈值For comparison, when the effective laser power density at a certain critical point is less than the abrasive laser removal energy threshold, the length from the starting point of the shaping trajectory to the critical point is defined as the initial trajectory length L0.

[0057] Furthermore, in step 3, during shaping, due to the continuous adjustment of the focal position of the laser beam, the defocus amount and the incident angle change rapidly during the shaping process, and the power density of each point on the trajectory line also changes in real time. In theory, the trajectory needs to be redesigned once each time the focal position is adjusted, which makes the trajectory design complicated and cumbersome. In order to reduce the number of trajectories and achieve the purpose of efficient removal of diamond abrasives, the method of setting trajectory increments can be used to avoid the disadvantages of repeatedly designing trajectories. However, the setting of trajectory increments must meet certain conditions. Generally, the shorter the length of the trajectory increment, the higher the shaping efficiency, but the number of corresponding planned trajectories will increase. Conversely, the longer the length of the trajectory increment, the lower the shaping efficiency. The length of the trajectory increment mainly depends on the focus adjustment position. Since the Gaussian beam can be approximately considered to be parallel within the Rayleigh length, the collimation is good, therefore, the focus adjustment distance can be set to a fixed value each time, i.e., 1 Rayleigh length. After designing the initial trajectory and trajectory increment, the laser effective power density is recalculated along the trajectory line and compared with the laser removal energy threshold of the diamond abrasive. When the laser effective power density is less than the diamond abrasive removal energy threshold, the critical point is recorded, and the length of the line segment from the end point of the L0 line segment to the critical point is the trajectory increment length L1.

[0058] Furthermore, in step 4, each time the Rayleigh length is adjusted, the focus position changes once, and the laser effective power density needs to be recalculated once. After finding the critical point, a trajectory increment is added. The first shaping trajectory is L0+L1, the second is L0+L1+L2, and the nth is L0+L1+…+L n .

[0059] Furthermore, in step 5, the spectrometer is turned on to collect a timing diagram reflecting the intensity change of the characteristic spectral line of the diamond, and the time required from the start of shaping (contact of the laser beam with the grinding wheel) to the absence of material removal on the grinding wheel surface is recorded. According to the shaping time and the laser scanning speed, the corresponding track length is calculated, and the experimental length value is compared with the theoretical calculated length value. After verifying the initial track length, adjust 1 Rayleigh length each time along the negative direction of the Z axis, verify the subsequent tracks in sequence, and finally determine the rationality of the length of each shaping track.

[0060] Furthermore, in step 6, the laser spot overlap rate / scanning track line overlap rate has an important influence on the contour accuracy of the grinding wheel after shaping. The higher the overlap rate, the higher the contour accuracy of the grinding wheel after shaping. The initial laser scanning track point and line overlap rate formula can be expressed as:

[0061]

[0062] Where d is the focal spot radius, v is the laser beam scanning speed, n is the grinding wheel speed, and f is the pulse repetition frequency.

[0063] Furthermore, it is designed to increase the overlap rate of laser scanning trajectories by adding new laser scanning trajectories. When the number of laser scanning trajectories added is n′, the overlap rate of the new laser scanning trajectories can be expressed as:

[0064]

[0065] n' is an integer

[0066] Where n′ is the number of added laser scanning trajectory lines, which is an integer.

[0067] Furthermore, it is designed to increase the overlap rate of laser spots by adding new laser spots. When the number of laser spots is increased to s, the overlap rate of the new laser spots can be expressed as:

[0068]

[0069] s is an integer

[0070] Where s is the number of laser spots added and is an integer.

[0071] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0072] 1. High shaping efficiency

[0073] During shaping, the laser beam needs to repeatedly scan the grinding wheel material along the shaping trajectory. In the later stage of shaping, as the incident angle and defocus amount increase, the laser irradiation spot area continues to increase, and the effective power density continues to decrease. When it is lower than the laser removal energy threshold of the abrasive particles, the laser beam cannot remove the diamond abrasive particles, and the laser beam will go idly along the shaping trajectory without removing the diamond abrasive particles. Therefore, how to design the laser shaping trajectory directly determines the efficiency of the laser shaping grinding wheel. The present invention plans the laser shaping trajectory of the formed grinding wheel, and takes the fact that the laser beam cannot remove the abrasive particles after the laser effective power density is less than the abrasive particle laser removal energy threshold as the trajectory planning basis, and establishes a theoretical model of the laser effective power density and the abrasive particle laser removal energy threshold. The length of each trajectory after actual planning is less than the original trajectory length, which avoids the situation that the laser beam still has to go idly along a section of the trajectory after failing to remove the abrasive particles in the later stage, shortens the actual laser processing time, and improves the shaping efficiency.

[0074] 2. High shaping accuracy

[0075] The laser spot overlap rate / scanning trajectory overlap rate has an important influence on the contour accuracy of the grinding wheel after shaping. The higher the overlap rate, the higher the contour accuracy of the grinding wheel after shaping. From the overlap rate formula, it can be seen that its size is usually affected by the inherent parameters of the equipment such as the focal spot radius d, the laser beam scanning speed v, the pulse repetition frequency f, and the grinding wheel speed n. The actual laser scanning trajectory point / line overlap rate is low, resulting in low shaping accuracy. This method can improve the laser spot overlap rate and the scanning trajectory line overlap rate by designing a laser multi-scanning trajectory, thereby ultimately improving the contour accuracy of the grinding wheel.

[0076] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The accompanying drawings are part of this application and are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but do not constitute an improper limitation of the present invention. Obviously, the drawings described below are only some embodiments. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0078] Figure 1 This is a schematic diagram of the laser shaping process in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of laser shaping trajectory planning in an embodiment of the present invention;

[0080] Figure 3 In the embodiment of the present invention Figure 2 A partial enlarged view of the middle A part;

[0081] Figure 4 This is a schematic diagram of the laser irradiation area in an embodiment of the present invention;

[0082] Figure 5 Schematic diagram of the incident angle of the laser beam in the embodiment of the present invention;

[0083] Figure 6 This is a schematic diagram of multiple scanning trajectories in an embodiment of the present invention;

[0084] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0086] Embodiment 1

[0087] As attached Figures 1 to 6 As shown, the forming grinding wheel laser shaping trajectory planning method described in this embodiment specifically includes the following steps:

[0088] Step 1: planning the laser shaping trajectory of the forming grinding wheel, as shown in the attached Figure 1-3 As shown. Since the V-shaped grinding wheel shaping trajectory is symmetrical, it can be divided into left and right sides. Taking the right half as an example, the laser shaping trajectory planning is carried out, and its total planning length can be expressed as:

[0089] L=L0+L1+L2+···+L n

[0090] Step 2: Determine the laser removal energy threshold E of the abrasive particles 阈值 ;

[0091]

[0092] In the formula, is the laser energy density at the center of the beam, which can be expressed as: e p is the single pulse energy. ω0 is the spot radius of the laser beam at the focus. w is the width of the ablation pit / groove. When w = 0, Equal to the laser energy density at the center of the beam

[0093] Taking the logarithm of both sides of the above equation yields:

[0094]

[0095] By performing a single-pass laser ablation experiment on the surface of a grinding wheel block, using an ultra-depth-of-field microscope to measure w, and then fitting the laser single pulse energy logarithm lne p With w 2 The linear relationship between the two is that if w = 0, the ablation threshold E of the abrasive material can be calculated. 阈值 .

[0096] Step 3: Determine the effective laser power density I at each point on the shaping trajectory A ;

[0097] I A =I p ×A c

[0098] In the formula, A c is the laser absorption rate, I p is the laser irradiation power density, which can be expressed as:

[0099]

[0100] Where P avg is the average power of the laser, f is the pulse repetition frequency, τ is the pulse width, and Per is the ratio of the laser power irradiated on the grinding wheel surface to the power emitted by the laser

[0101] When the laser beam is incident along the Z-axis direction, Figure 4 As shown, the surface of the profiled grinding wheel is located in the spatial coordinate system O-XOY.

[0102] For a V-shaped grinding wheel, the laser scanning trajectory equation in the XOY plane is:

[0103]

[0104] Where θ is the V-shaped grinding wheel tip angle, B is the grinding wheel width, and R0 is the grinding wheel edge radius.

[0105] Initial parallel to the upper surface of the grinding wheel (above the XOY plane) equation:

[0106]

[0107] Where R is the radius of the grinding wheel

[0108] Fundamental mode Gaussian laser beam equation:

[0109]

[0110] In the formula, ω0 is the radius of the laser beam spot at the focus. (i.e., the radius of the laser beam "waist"), x0, y0, z0 are the coordinate values ​​at the focus, r is the radius of the laser beam spot at coordinate Z, and λ is the wavelength.

[0111] The irradiation spot area of ​​the laser beam on the parallel grinding wheel is:

[0112]

[0113] Where R is the radius of the grinding wheel, D xy is the projection area of ​​the laser beam irradiated surface in the XOY plane. The integration domains of x and y are:

[0114]

[0115] The ratio of the laser power irradiated on the grinding wheel surface to the laser power emitted is:

[0116]

[0117] In the XOY plane, the profile line equation of the grinding wheel shaft section is:

[0118] y=R,

[0119] The cross-section profile of the shaft rotates around the X-axis to obtain the surface equation of the grinding wheel:

[0120] z 2 =R 2 -y 2

[0121] make:

[0122] f(x,y,z)=-R 2 +y 2 +z 2

[0123] Normal vector of the grinding wheel surface at any point:

[0124]

[0125] The laser incident angle refers to the angle between the center line of the laser beam and the outer normal of the grinding wheel surface at the laser incident point. Take the upper surface of the forming grinding wheel (above the XOY plane) for analysis. Since the center line of the laser beam is parallel to the Z axis, its unit vector is Combined with the external normal vector n of the grinding wheel surface at the laser incident point, according to the space vector and The angle formula can be used to calculate the incident angle of the laser beam.

[0126]

[0127] In the formula, m x ,m y ,m z Represents the projection of the space vector m on the x-axis, y-axis, and z-axis, n x ,n y ,n z Represents the projection of the space vector n on the x-axis, y-axis, and z-axis

[0128] Laser absorption rate A c It can be expressed as:

[0129]

[0130] In the formula, i is the refractive index and k is the extinction coefficient

[0131] Step 4: Compare the effective power density I of the laser point by point along the trajectory line. A The energy threshold E of abrasive laser removal 阈值 When the effective laser power density at a certain critical point is less than the abrasive laser removal energy threshold, the length from the starting point of the shaping trajectory to the critical point is defined as the initial trajectory length L0.

[0132] Step 5, after adjusting the focus by 1 Rayleigh length, calculate the effective power density of the laser at each point along the trajectory again, and compare it with the laser removal energy threshold point of the diamond abrasive. When it is less than the diamond abrasive removal energy threshold, record the critical point, and the length of the line segment between the end point of L0 and the critical point is the trajectory increment length L1.

[0133] Step 6: Each time the Rayleigh length is adjusted, the focus position changes once, and the effective power density of the laser needs to be recalculated once. After finding the critical point, a trajectory increment is added. The first shaping trajectory is L0+L1, the second is L0+L1+L2, and the nth is L0+L1+…+L n .

[0134] Step 7, turn on the spectrometer, collect a time sequence diagram reflecting the changes in the intensity of the diamond characteristic spectral line, and record the time required from the start of shaping (the laser beam contacts the grinding wheel) to the absence of material removal on the grinding wheel surface. According to the shaping time and the laser scanning speed, calculate the corresponding track length, and compare the experimental length value with the theoretical calculated length value. After verifying the initial track length, adjust 1 Rayleigh length each time along the negative direction of the Z axis, verify the subsequent tracks in sequence, and finally determine the rationality of the length of each shaping track.

[0135] Step 8: Based on the initially set laser scanning trajectory overlap rate, the laser scanning trajectory overlap rate is increased by adding new scanning trajectory lines. Figure 6 As shown, the initial scanning trajectory line overlap rate is set to -50%, the target scanning trajectory line overlap rate is 25%, and the number of scanning trajectory lines is increased to 2.

[0136] Step 9: Based on the initially set laser spot overlap rate, the laser spot overlap rate is increased by adding new laser spots. The initial laser spot overlap rate is set to -50%, the target laser spot overlap rate is set to 25%, and the number of laser spots is increased to 2.

[0137] After laser shaping of the V-shaped grinding wheel by using the method of scientifically planning the laser shaping trajectory of the forming grinding wheel, the shaping efficiency and shaping accuracy are greatly improved.

[0138] The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment, it is not used to limit the present invention. Any technician familiar with this patent can make some changes or modify the technical contents suggested above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the solution of the present invention.

Claims

1. A method for planning the trajectory of laser shaping of a forming grinding wheel, characterized in that: The following steps are involved: Step 1: Since the V-shaped grinding wheel shaping trajectory is symmetrical, it can be divided into left and right sides, and the laser shaping trajectory design is carried out taking the right half as an example; Step 2: Establish a theoretical model of laser effective power density and abrasive laser removal energy threshold to determine the initial track length. The initial track length L0 is designed to depend on the laser effective power density I A The energy threshold E of laser removal of abrasive particles 阈值 , the energy threshold E for abrasive laser removal 阈值 It can be expressed as: Where ω0 is the spot radius of the laser beam at the focus, w is the diameter of the ablation pit or the width of the groove on the abrasive surface, and the laser energy density at the edge of the ablation pit or the edge of the groove is: This is the minimum laser energy required to remove abrasive materials; when w = 0, Equal to the laser energy density at the center of the beam e p is the single pulse energy, Taking the logarithm of the above formula: By performing a single-pass laser ablation experiment on the surface of a grinding wheel block, using an ultra-depth-of-field microscope to measure w, and then fitting the laser single pulse energy logarithm lne p With w 2 The linear relationship between the two is that if w = 0, the ablation threshold of the abrasive material can be calculated. Step 3: To further improve the dressing efficiency, design the trajectory increment and plan its length; Step 4, planning the remaining shaping trajectories until all laser shaping trajectories are planned; Step 5, using a spectrometer to collect the intensity of diamond characteristic spectral lines to verify the rationality of the trajectory planning path; Step 6: Design laser multi-scanning trajectories to increase the laser spot overlap rate and the scanning trajectory line overlap rate.

2. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 1, the laser shaping track length L can be expressed as: <h2 style=";text-align:left;direction:ltr">L = L0 + L1 + L2 + · · · + L<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> 。 3. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 2, the laser effective power density I A It can be expressed as: I A =I p ×A c In the formula, I p is the laser irradiation power density, A c is the laser absorptivity; Laser irradiation power density I p It can be expressed as: Where P avg is the average power of the laser, f is the pulse repetition frequency, τ is the pulse width, Per is the ratio of the laser power irradiated on the grinding wheel surface to the power emitted by the laser, S p is the irradiation spot area; For a V-shaped grinding wheel, the laser scanning trajectory equation in the XOY plane is: Where θ is the V-shaped grinding wheel tip angle, B is the grinding wheel width, and R0 is the grinding wheel edge radius; Parallel to the upper surface equation of the grinding wheel: Where R is the radius of the grinding wheel Fundamental mode Gaussian laser beam equation: Where ω0 is the spot radius of the laser beam at the focus; x0, y0, z0 are the coordinate values ​​of the laser focus, r is the spot radius of the laser beam at the coordinate Z, and λ is the wavelength; The irradiation spot area of ​​the laser beam on the parallel grinding wheel is: Where R is the radius of the grinding wheel, D xy is the projection area of ​​the laser beam irradiated surface in the XOY plane; the integration domains of x and y are: The ratio of the laser power irradiated on the grinding wheel surface to the power emitted by the laser is: In the XOY plane, the profile line equation of the grinding wheel shaft section is: The cross-section profile of the shaft rotates around the X-axis to obtain the surface equation of the grinding wheel: z 2 =R 2 -y 2 make: f(x,y,z)=-R 2 +y 2 +z 2 Normal vector of the grinding wheel surface at any point: The laser incident angle refers to the angle between the center line of the laser beam and the outer normal of the grinding wheel surface at the laser incident point; the upper surface of the forming grinding wheel is analyzed. Since the center line of the laser beam is parallel to the Z axis, its unit vector is Combined with the external normal vector n of the grinding wheel surface at the laser incident point, according to the space vector and The angle formula can be used to calculate the incident angle of the laser beam; In the formula, m x ,m y ,m z Represents the projection of the space vector m on the x-axis, y-axis, and z-axis, n x ,n y ,n z Represents the projection of the space vector n on the x-axis, y-axis, and z-axis; Laser absorption rate A c It can be expressed as: Where i is the refractive index and k is the extinction coefficient.

4. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 2, the laser effective power density I is calculated point by point along the laser shaping trajectory. A and the abrasive laser removal energy threshold E 阈值 For comparison, when the effective laser power density at a certain critical point is less than the abrasive laser removal energy threshold, the length from the starting point of the shaping trajectory to the critical point is defined as the initial trajectory length L0.

5. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 3, the trajectory increment is planned in the following way: the focus adjustment distance is set to a fixed value each time, i.e., 1 Rayleigh length. After the initial trajectory and trajectory increment are planned, the laser effective power density is recalculated along the trajectory line and compared with the laser removal energy threshold of the diamond abrasive. When the laser effective power density is less than the diamond abrasive removal energy threshold, the critical point is recorded. The length of the line segment between the end point of L0 and the critical point at this time is the trajectory increment length L1.

6. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 4, each time the Rayleigh length is adjusted, the focus position changes once, and the laser effective power density needs to be recalculated once. After the critical point is found, a trajectory increment is added; the first shaping trajectory is L0+L1, the second is L0+L1+L2, and the nth is L0+L1+…+L n .

7. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 5, turn on the spectrometer, collect a time series diagram reflecting the intensity changes of the diamond characteristic spectral lines, and record the time required from the start of shaping to the absence of material removal on the grinding wheel surface; calculate the corresponding track length based on the shaping time and the laser scanning speed, and compare the experimental length value with the theoretical calculated length value; after verifying the initial track length, adjust 1 Rayleigh length each time along the negative direction of the Z axis, verify the subsequent tracks in sequence, and finally determine the rationality of the length of each shaping track.

8. The method for planning trajectory of laser shaping of a forming grinding wheel according to claim 1, characterized in that: In step 5, the initial laser scanning trajectory point and line overlap formula can be expressed as: Where d is the focal spot radius, v is the laser beam scanning speed, n is the grinding wheel speed, and f is the pulse repetition frequency. The design adds new laser scanning trajectories to improve the overlap rate of laser scanning trajectories. When the number of laser scanning trajectories is n′, the overlap rate of the new laser scanning trajectories can be expressed as: P>P x , n′ is an integer In the formula, n′ is the number of lines added to the laser scanning trajectory, which is an integer; It is designed to increase the laser spot overlap rate by adding new laser spots. When the number of laser spots is increased to s, the new laser spot overlap rate can be expressed as: M>M x , s is an integer Where s is the number of laser spots added and is an integer.

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