Three-dimensional laser welding head
By combining high-power lasers and various optical structures, multiple welding focal points of different depths are formed, solving the problem of low-cost, high-efficiency, and high-power three-dimensional laser welding in existing technologies, and realizing high-precision and high-efficiency three-dimensional laser welding.
Patent Information
- Application Number
- CN202511416745.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-30
- Publication Date
- 2025-11-11
AI Technical Summary
Existing technologies struggle to achieve low-cost, high-efficiency, and high-power 3D laser welding. Multi-axis robot systems and optical control technologies have failed to achieve true 3D synchronous welding, and spatial light modulators are costly and complex to control.
By combining a high-power laser, collimating lens, laser beam splitting structure, reflection structure, laser beam combining structure and focusing structure, multiple welding focal points of different depths are formed, and three-dimensional laser welding is achieved using a single laser welding head.
It enables high-precision and high-efficiency three-dimensional laser welding, reduces equipment costs, and increases the compatibility and versatility of laser welding.
Smart Images

Figure CN120920901A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of laser welding, and in particular to a three-dimensional laser welding head. Background Technology
[0002] Due to the rigid requirements of complex structure manufacturing, the contradiction between lightweight and high strength, and the trend towards high precision and automation, 3D laser welding has become an inevitable direction for the development of laser welding. Multiple fields have raised welding requirements for 3D laser welding. For example, components such as automobile bodies, aircraft tail fin panels, and rocket engine nozzles have complex 3D curved surfaces or internal cavity structures, making it difficult to achieve high-precision, seamless connections using traditional welding methods. Another example is multi-layer material welding, such as the welding of multi-layer tabs in new energy vehicle batteries, which requires simultaneous penetration of different material layers and control of the heat-affected zone to avoid delamination or deformation. In terms of high-precision and automated welding, precision electronic devices (such as the hermetically sealed assembly of 3D ceramic substrates) require micron-level weld seam control, and 3D laser welding combined with robotics technology can meet these requirements.
[0003] Achieving 3D laser welding is of great significance for process innovation, efficiency improvement, and industrial applications, and can achieve significant economic benefits. In terms of efficiency improvement, compared to traditional vacuum brazing, 3D laser welding reduces the nozzle manufacturing cycle from several weeks to 10 hours, lowering costs by more than 50%. 3D laser welding can be better integrated with automated welding, reducing reliance on manual labor. Equipment such as six-axis robotic welding machines can collaborate across multiple workstations, further enhancing production efficiency.
[0004] Currently, the main methods for achieving 3D laser welding are multi-axis robot collaborative control and optical control technology. Multi-axis robot collaborative control uses a six-axis / seven-axis robot system, achieving 3D welding with complex trajectories through the linkage of the robotic arm and the laser head. However, this type of 3D welding requires multiple welding equipment and multiple robots, increasing welding costs and reducing efficiency. Optical control technology includes dynamic zoom technology, integrating liquid lenses or Z-axis galvanometers to adjust the focal depth in real time to adapt to surface changes. However, this method only achieves changes in the welding focal length, not true 3D welding with different depths and multiple focal points. In addition, there is scanning galvanometer technology, where high-speed galvanometers enable rapid positioning of the laser beam in 3D space, combined with flying welding technology (such as laser flying welding) to improve long-distance welding efficiency. This 3D laser welding based on scanning galvanometers is essentially the same as focusing technology, moving within multiple planes in a short time, and also does not achieve true 3D synchronous laser welding. Currently, truly achieving 3D laser welding uses a spatial light modulator (SLM), generating multiple focal points through phase modulation to simultaneously process multi-layered materials or complex welds. However, due to the limitations of spatial light modulators themselves, such as low damage threshold, high cost, and complex control mechanism, three-dimensional laser welding based on spatial light modulators is difficult to achieve high-power laser welding and is difficult to apply on a large scale.
[0005] Therefore, low-cost, high-efficiency, and high-power three-dimensional laser welding remains an important challenge in the field of laser welding that needs to be addressed. Summary of the Invention
[0006] In order to overcome the above-mentioned defects of the prior art, the present invention provides a three-dimensional laser welding head to solve the problems existing in the background art.
[0007] This invention provides the following technical solution: a three-dimensional laser welding head, comprising: High-power lasers are used to provide high-power laser sources. A collimating lens, placed in the output direction of the laser source, is used to convert the passing laser into multiple non-intersecting collimated lasers; A laser beam splitting structure, positioned in the output direction of the collimating lens, is used to split a collimated laser beam into multiple beams. The reflective structure includes multiple mirrors, which are respectively placed in the transmission direction of each collimated laser beam to reflect multiple collimated laser beams to the same point for focusing. A laser beam combining structure is placed at the point after multiple collimated laser beams are reflected, so that the multiple collimated laser beams are combined and their transmission directions are consistent. The focusing structure includes multiple focusing mirrors, which are spaced apart along the direction of the reflected collimated laser. Multiple collimated laser beams pass through the focusing mirrors in front of them one by one, so that the collimated lasers are focused once or twice to form multiple focal points of different depths.
[0008] Preferably, the laser beam splitting structure is a first beam splitting prism, which is placed in the output direction of the collimating lens to receive the collimated laser and split it into a first collimated laser and a second collimated laser. The first collimated laser and the second collimated laser are transmitted along different propagation directions, and the angle between the propagation directions is 90°.
[0009] Preferably, the reflection structure consists of a first reflector and a second reflector. The first reflector is positioned in the transmission direction of the first collimated laser and reflects the first collimated laser by 90°. The second reflector is positioned in the transmission direction of the second collimated laser and reflects the second collimated laser by 90°, so as to form a vertical first collimated laser and a vertical second collimated laser.
[0010] Preferably, the laser beam combining structure is a first beam combining prism, which is positioned at the intersection of the first collimated laser and the second collimated laser, and is used to combine the passing first collimated laser and second collimated laser beams.
[0011] Preferably, the focusing structure comprises a first focusing lens and a second focusing lens. The first focusing lens is positioned in the transmission direction of the first collimated laser and is used to convert the passing first collimated laser into a first focused beam. The second focusing lens is positioned in the output direction of the first beam combiner prism and is used to convert the passing second collimated laser into a second focused beam and the passing first focused beam into a third focused beam, thereby forming two focusing points at different depths.
[0012] Preferably, the laser beam splitting structure further includes a second beam splitting prism, the laser beam combining structure further includes a second beam combining prism, and the focusing structure further includes a third focusing mirror. The second beam splitting prism is placed between the first beam splitting prism and the first reflecting mirror to split out the third collimated laser. The second beam combining prism is set in the transmission direction of the third collimated laser to combine the third collimated laser and the first focused beam. The third focusing mirror is set between the first beam combining prism and the second beam combining prism to focus the third collimated laser and the first focused beam to form three focusing points of different depths.
[0013] Preferably, the laser beam splitting structure is a first beam splitter, which is used to receive the collimated laser and split it into a first collimated laser and a second collimated laser. The laser beam combining structure is a first beam combiner, which is positioned at the perpendicular intersection of the first collimated laser and the second collimated laser, so that the first collimated laser and the second collimated laser are combined by passing through a beam combining prism, and the transmission directions of the first collimated laser and the second collimated laser are consistent.
[0014] Preferably, the laser beam splitting structure is a diffraction grating, which is placed in the output direction of the collimating lens to receive the collimated laser and diffract the first collimated laser and the second collimated laser. The reflection structure is a third mirror and a fourth mirror. The third mirror is placed in the transmission direction of the first collimated laser and reflects the first collimated laser by 90°. The fourth mirror is placed in the transmission direction of the second collimated laser and reflects the second collimated laser by 90°, so as to form the first collimated laser and the second collimated laser that intersect perpendicularly.
[0015] Preferably, the device further includes a first movable clamp and a second movable clamp, wherein the first movable clamp is used to hold the first focusing lens and the second movable clamp is used to hold the second focusing lens.
[0016] Preferably, the vortex laser is selected from one of the following: chrysoberyl laser, Nd:YAG laser, Yb:YAG laser, and Tm:YLF laser.
[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention uses a single high-power laser as the overall laser welding light source, achieving a high-precision and high-efficiency method for detecting turbulence intensity parameters. It also boasts advantages such as high detection accuracy, high efficiency, and cross-verification of detection results. Furthermore, by utilizing the coordination of collimating lenses, laser beam splitting structures, reflection structures, laser beam combining structures, and focusing structures, multiple welding focal points of different depths are formed, thereby realizing a three-dimensional laser welding laser beam. This not only reduces the cost of laser welding equipment but also achieves three-dimensional laser welding with a single laser welding head, increasing the compatibility and universality of laser welding. Attached Figure Description
[0018] Figure 1 This is a schematic diagram of the three-dimensional laser welding head structure of Embodiment 1 of the present invention.
[0019] Figure 2 This is a schematic diagram of the structure for changing the position of the focused beam according to the present invention.
[0020] Figure 3 This is a schematic diagram of the three-dimensional laser welding head structure of Embodiment 2 of the present invention.
[0021] Figure 4 This is a schematic diagram of the three-dimensional laser welding head structure of Embodiment 3 of the present invention.
[0022] Figure 5 This is a schematic diagram of the three-dimensional laser welding head structure of Embodiment 4 of the present invention.
[0023] Figure 6 This is a schematic diagram of the three-dimensional laser welding head structure of Embodiment 5 of the present invention.
[0024] Figure 7 This is a schematic diagram of the focused beam in a coaxial state according to the present invention.
[0025] Figure 8 This is a schematic diagram of the focused beam under different axis states of the present invention.
[0026] The attached figures are labeled as follows: 1. Laser source; 2. Collimating lens; 3. First beam splitter prism; 4. First reflecting mirror; 5. Second reflecting mirror; 6. First focusing mirror; 7. First beam combiner prism; 8. Second focusing mirror; 9. First welding workpiece; 10. Second welding workpiece; 11. Third welding workpiece; 12. Second beam splitter prism; 13-1. Second beam combiner prism; 13-2. Third focusing mirror; 14. First beam splitter prism; 15. First beam combiner prism; 16. Diffraction grating; 17. Third reflecting mirror; 18. Fourth reflecting mirror; 19. First movable fixture; 20. Second movable fixture. Detailed Implementation
[0027] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.
[0028] Using a single laser welding light source as the overall welding light source, to achieve three-dimensional laser welding, multiple laser beams need to be focused at different depths.
[0029] Example 1
[0030] A three-dimensional laser welding head can achieve three-dimensional laser welding with two focal planes, such as... Figure 1 As shown, it includes a laser source 1, a collimating lens 2, a first beam splitter prism 3, a first reflecting mirror 4, a second reflecting mirror 5, a first focusing mirror 6, a first beam combiner prism 7, and a second focusing mirror 8.
[0031] The goal is to simultaneously weld the first welding workpiece 9 to the second welding workpiece 10 and the second welding workpiece 11. Here, the weld depth between the first welding workpiece 9 and the second welding workpiece 10 differs from the weld depth between the second welding workpiece 10 and the third welding workpiece 11. Furthermore, the weld strength between the first welding workpiece 9 and the second welding workpiece 10 also differs from the weld strength between the second welding workpiece 10 and the third welding workpiece 11. This is due to the different welding requirements and the different power requirements of the different welding materials.
[0032] Vortex laser 1 provides a high-power laser source for the entire laser welding system, outputting welding laser light. One of the following can be selected: an chromosome-enriched vortex laser, an Nd:YAG laser, a Yb:YAG laser, or a Tm:YLF laser. Using a vortex laser as the light source for turbulence intensity parameter detection achieves a high-precision and high-efficiency method for detecting turbulence intensity parameters, while also offering advantages such as high detection accuracy, high efficiency, and cross-verification of detection results.
[0033] Collimating lens 2 is positioned in the output direction of the laser source. Since the welding laser is divergent, the welding laser becomes collimated after passing through collimating lens 2.
[0034] The first beam splitter prism 3 is positioned in the output direction of the collimating mirror to receive the collimated laser. The collimated welding laser is then split into two perpendicular welding laser beams by the first beam splitter prism 3. The two laser beams propagate along different propagation directions with an angle of 90° between them.
[0035] These two vertical welding laser beams are the basis for achieving two different focal depths (different focal planes). For ease of understanding, the two laser beams will be referred to as the first collimated laser and the second collimated laser, respectively.
[0036] The first reflector 4 is positioned in the transmission direction of the first collimated laser, thereby reflecting the first collimated laser and rotating its propagation direction by 90°. The second reflector 5 is positioned in the transmission direction of the second collimated laser, thereby reflecting the second collimated laser and rotating its propagation direction by 90°.
[0037] The first beam combiner prism 7 is positioned at the intersection of the first collimated laser and the second collimated laser, the first focusing lens 6 is positioned in the transmission direction of the first collimated laser, and the second focusing lens 8 is positioned in the transmission direction of the first beam combiner prism 7.
[0038] The first collimated laser propagates losslessly and without modulation to the first beam combiner prism 7, where it remains collimated. The second collimated laser, after being reflected by the second reflector 5, reaches the first focusing mirror 6, which focuses the second collimated laser to form the first focused laser used for welding. The first focused laser also reaches the first beam combiner prism 7. The propagation angle of the first collimated laser shifts by 90° after passing through the first beam combiner prism 7, while the propagation direction of the first focused laser remains unchanged. At this point, the first collimated laser and the first focused laser are coaxial and reach the second focusing mirror 8.
[0039] Since the first collimated laser is not focused, while the first focused laser is partially focused, it transforms into a third focused laser after passing through the second focusing lens 8. Because the first focused laser already shows a tendency to focus, the focal point of the third focused laser is shorter than that of the second focused laser, resulting in welding lasers with different focal depths, thus realizing a laser beam for three-dimensional laser welding.
[0040] It can be said that during the three-dimensional laser welding process, the different distances between the first focusing mirror 6 and the second focusing mirror 8 result in different relative focal points for the second and third focused beams. When the distance between the first focusing mirror 6 and the second focusing mirror 8 is relatively close, the first focused beam is not yet fully focused. After passing through the second focusing mirror 8, the laser is further focused, and the focal point of the resulting third focused beam is above that of the second focused beam.
[0041] If the distance between the first focusing lens 6 and the second focusing lens 8 is far, the first focusing beam has already been focused and diverged. At this time, the first focusing laser is divergent. After passing through the second focusing lens 8, the laser focusing degree is low, and the focal point of the third focusing beam is below the second focusing beam.
[0042] Example 2
[0043] A three-dimensional laser welding head can achieve three-dimensional laser welding with three focal planes, such as... Figure 3 As shown, the main difference from Embodiment 1 is that it also includes a second beam splitter prism 12, a second beam combiner prism 13-1, and a third focusing lens 13-2.
[0044] The second beam-splitting prism 12 is positioned between the first beam-splitting prism 3 and the first reflecting mirror 4, causing the first collimated beam to be split into two laser beams again after passing through the second beam-splitting prism 12. One laser beam (i.e., the first collimated laser) propagates along the original optical path. For ease of understanding, the other laser beam is called the third collimated laser. The third collimated laser and the first focused beam form a focal point.
[0045] The second beam combiner prism 13-1 is positioned at the focal point, so that the third collimated laser and the first focused beam are combined after passing through the second beam combiner prism 13-1, that is, the third collimated laser and the first focused beam are coaxial.
[0046] The third focusing mirror 13-2 is positioned in the transmission direction of the beam combining mechanism, allowing the third collimated laser and the first focused laser to pass together through the third focusing mirror 13-2. The third collimated laser is focused to form the fourth focused laser, and the first focused laser is focused to form the third focused laser. Since the first focused beam has already been focused, it has a shorter focal length, while the third collimated laser has a longer focal length.
[0047] After beam combining, the laser beam is combined with the second collimated laser by the first beam combining prism 7, and then focused for the last time by the second focusing lens 8. At this time, the fourth focusing laser is focused to form the fifth focusing laser, the third focusing laser is focused to form the sixth focusing laser, and the first collimated laser is focused to form the second focusing laser (that is, the first collimated laser is focused once, the second collimated laser is focused three times, and the third collimated laser is focused twice), so as to form three welding lasers with different focal lengths, forming a three-dimensional laser welding beam with three focal planes.
[0048] The cooperation between the second beam splitter prism 12, the second beam combiner prism 13-1, and the third focusing lens 13-2 achieves three focusing points at different depths, enabling simultaneous welding of three weld seams. The principle is the same as that of simultaneously welding two weld seams in Example 1.
[0049] Example 3
[0050] A three-dimensional laser welding head, employing a beam-splitting mirror to achieve three-dimensional welding, is designed as follows: Figure 4 As shown, the main difference from Embodiment 1 is that the first beam splitter 14 and the first beam combiner 15 are used instead of the first beam splitter prism 3 and the first beam combiner prism 7. The functions of the first beam splitter 14 and the first beam combiner 15 are the same as those of the first beam splitter prism and the first beam combiner prism, but the beam splitting principle of the beam splitter is usually achieved by coating to achieve partial transmission.
[0051] Furthermore, by using a coated beam splitter, different ratios of beam splitting can be achieved, resulting in welding beams with different focusing powers.
[0052] Example 4
[0053] A three-dimensional laser welding head, the structure of which is designed using a diffraction grating, such as... Figure 5 As shown, the main difference in Embodiment 1 is that a diffraction grating 16 is added, and a third reflecting mirror 17 and a fourth reflecting mirror 18 are used instead of the first reflecting mirror 4 and the second reflecting mirror 5.
[0054] The diffraction grating 16 can diffract the original laser into different orders at different angles through laser diffraction. These different orders have different powers and directions. The laser beams of different orders are then reflected back to the same optical axis by the third reflecting mirror 17 and the fourth reflecting mirror 18. Because the reflection angles are different, the laser beams reach different heights. By placing the first focusing mirror 6 between the third reflecting mirror 17 and the fourth reflecting mirror 18, a portion of the laser beam can be focused. The achieved effect is the same as in Embodiment 1, but the structure is more compact.
[0055] Example 5
[0056] A three-dimensional laser welding head, with a laser welding head structure design that enables adjustable focal length three-dimensional welding, such as... Figure 6 As shown, the main difference from Embodiment 1 is that a first movable clamp 19 and a second movable clamp 20 are added.
[0057] The first movable clamp 19 is used to hold the first focusing lens 6, and can move in the up, down, left, and right directions. The second movable clamp 20 is used to hold the second focusing lens 8, and can move in the up, down, left, and right directions. By moving it up and down, the distance between the first focusing lens 6 and the second focusing lens 8 can be adjusted, further changing the focal length of the third focused beam.
[0058] Furthermore, it enables non-axial focusing. By changing the positions of the first focusing lens 6 and the second focusing lens 8, the laser can be deviated from its original optical axis position, achieving focusing at different cross-sections and enabling more flexible three-dimensional laser welding.
[0059] In a coaxial state, such as Figure 7 As shown, the first welding workpiece 9 and the second welding workpiece 10 are adjacent to each other, while the second welding workpiece 10 and the second welding workpiece 11 are stacked. Their welds have a height difference, but form a vertical state with corresponding top and bottom.
[0060] Under different axis conditions, such as Figure 8 As shown, the first welded workpiece 9, the second welded workpiece 10, and the second welded workpiece 11 are stacked in a stepped manner, and their welds have a height difference, but they are not vertically aligned side by side.
[0061] Several points should be noted: First, in the description of this application, it should be noted that, unless otherwise specified and limited, the terms "installation", "connection" and "linkage" should be interpreted broadly, and can be mechanical or electrical connection, or internal connection between two components, or direct connection. "Up", "down", "left", "right", etc. are only used to indicate relative positional relationship. When the absolute position of the described object changes, the relative positional relationship may change.
[0062] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.
Claims
1. A three-dimensional laser welding head, characterized in that, include: High-power lasers are used to provide high-power laser sources. A collimating lens, placed in the output direction of the laser source, is used to convert the passing laser into multiple non-intersecting collimated lasers; A laser beam splitting structure, positioned in the output direction of the collimating lens, is used to split a collimated laser beam into multiple beams. The reflective structure includes multiple mirrors, which are respectively placed in the transmission direction of each collimated laser beam to reflect multiple collimated laser beams to the same point for focusing. A laser beam combining structure is placed at the point after multiple collimated laser beams are reflected, so that the multiple collimated laser beams are combined and their transmission directions are consistent. The focusing structure includes multiple focusing mirrors, which are spaced apart along the direction of the reflected collimated laser. Multiple collimated laser beams pass through the focusing mirrors in front of them one by one, so that the collimated lasers are focused once or twice to form multiple focal points of different depths.
2. The three-dimensional laser welding head according to claim 1, characterized in that: The laser beam splitting structure is a first beam splitting prism, which is placed in the output direction of the collimating lens to receive the collimated laser and split it into a first collimated laser and a second collimated laser. The first collimated laser and the second collimated laser are transmitted along different propagation directions, and the angle between the propagation directions is 90°.
3. A three-dimensional laser welding head according to claim 2, characterized in that: The reflection structure consists of a first reflector and a second reflector. The first reflector is positioned in the transmission direction of the first collimated laser and reflects the first collimated laser by 90°. The second reflector is positioned in the transmission direction of the second collimated laser and reflects the second collimated laser by 90°, so as to form a vertical first collimated laser and a vertical second collimated laser.
4. A three-dimensional laser welding head according to claim 3, characterized in that: The laser beam combining structure is a first beam combining prism, which is positioned at the intersection of the first collimated laser and the second collimated laser, and is used to combine the passing first collimated laser and the second collimated laser into a single beam.
5. A three-dimensional laser welding head according to claim 4, characterized in that: The focusing structure consists of a first focusing lens and a second focusing lens. The first focusing lens is positioned in the transmission direction of the first collimated laser and is used to convert the passing first collimated laser into a first focused beam. The second focusing lens is positioned in the output direction of the first beam combiner prism and is used to convert the passing second collimated laser into a second focused beam and the passing first focused beam into a third focused beam, so as to form two focusing points at different depths.
6. A three-dimensional laser welding head according to claim 5, characterized in that: The laser beam splitting structure further includes a second beam splitting prism, the laser beam combining structure further includes a second beam combining prism, and the focusing structure further includes a third focusing mirror. The second beam splitting prism is placed between the first beam splitting prism and the first reflecting mirror to split out the third collimated laser. The second beam combining prism is set in the transmission direction of the third collimated laser to combine the third collimated laser and the first focused beam. The third focusing mirror is set between the first beam combining prism and the second beam combining prism to focus the third collimated laser and the first focused beam to form three focusing points of different depths.
7. A three-dimensional laser welding head according to claim 1, characterized in that: The laser beam splitting structure is a first beam splitter, which receives the collimated laser and splits it into a first collimated laser and a second collimated laser. The laser beam combining structure is a first beam combiner, which is positioned at the perpendicular intersection of the first and second collimated lasers, so that the first and second collimated lasers are combined by passing through a beam combining prism, and the transmission directions of the first and second collimated lasers are consistent.
8. A three-dimensional laser welding head according to claim 1, characterized in that: The laser beam splitting structure is a diffraction grating, which is placed in the output direction of the collimating mirror to receive the collimated laser and diffract the first collimated laser and the second collimated laser. The reflection structure consists of a third mirror and a fourth mirror. The third mirror is placed in the transmission direction of the first collimated laser and reflects the first collimated laser by 90°. The fourth mirror is placed in the transmission direction of the second collimated laser and reflects the second collimated laser by 90°, so as to form the first collimated laser and the second collimated laser that intersect perpendicularly.
9. A three-dimensional laser welding head according to claim 2, characterized in that: It also includes a first movable clamp and a second movable clamp, wherein the first movable clamp is used to hold the first focusing lens and the second movable clamp is used to hold the second focusing lens.
10. A three-dimensional laser welding head according to claim 1, characterized in that: The vortex laser is selected from one of the following: chrysoberyl laser, Nd:YAG laser, Yb:YAG laser, and Tm:YLF laser.
Citation Information
Patent Citations
Laser processing of transparent article using multiple foci
CN107107267A
Coaxial double-beam swinging laser hybrid welding device and method
CN117600653A
Outer-layer focus rotation auxiliary high-power laser hybrid welding device
CN119407322A
Method for providing to a processing device, method for controlling a processing device, control device, processing device, computer program and computer-readable medium
DE102023104354A1