Optimization method for manufacturing rotary deployable curved surface PCB

Abstract

The invention relates to an optimization method for manufacturing a rotary deployable curved plate, which belongs to the technical field of printed circuit board manufacturing, and comprises the following steps of: converting 3D (three-dimensional) coordinates of a client into 2D (two-dimensional) coordinates according to a 3D-2D (three-dimensional) transformation formula of coordinates corresponding to the appearance of a curved PCB (printed circuit board) to obtain a D code manuscript containing the positions, shapes or sizes of holes, bonding pads and leads during graph display and wiring, and realizing curvature adaptation of graph transfer; then, a curved surface supporting mold is used for being attached to the back face of the curved surface PCB, it is ensured that a base material is free of local collapse during drilling, meanwhile, a temporary back plate is added to enhance local rigidity, and curvature constraint before drilling is achieved; coordinates in the hole dividing graph are converted into cylindrical coordinates through a corresponding coordinate 2D-3D conversion formula, a drilling coordinate file and a 3D tool path file are generated, a drill bit or an end mill always points to the projection of a hole site on a generatrix, it is ensured that the hole site precision is matched with the curvature of a milling plate after rewinding, and low-rotating-speed high-feeding segmented pecking drilling is adopted, so that the machining precision is improved. Heat accumulation and lateral force are reduced.

Description

Technical Field

[0001] This invention belongs to the technical field of printed circuit board manufacturing, and particularly relates to an optimized method for manufacturing rotatable surface PCBs. Background Technology

[0002] A standard circuit board has zero curvature and an infinite radius of curvature. All holes drilled on the board are perpendicular to the board plane and parallel to each other in the same direction to prevent deformation. However, a developable panel has non-zero curvature and an infinite radius of curvature. If holes are drilled in the same way as a straight board, the curved panel will inevitably deform, or even produce deformed holes.

[0003] In the fabrication of developable PCBs (such as cylindrical or conical surfaces that can be unfolded into flat surfaces), especially in the drilling and routing steps, it is necessary to deeply integrate the geometric characteristics of the curved surface with precision machining technology. High-precision manufacturing under curvature constraints can be achieved through material adaptation, dynamic path planning, high-stability tooling, and non-contact processing (laser). The core challenge lies in how to balance processing stress and geometric accuracy. It is necessary to continuously optimize process parameters by combining finite element analysis (FEA) and real-time monitoring technology. Curvature constraints, drilling, and routing are key steps to ensure geometric accuracy and functionality. Summary of the Invention

[0004] The purpose of this invention is to provide an optimized method for manufacturing a rotary developable PCB, which optimizes the curvature constraint, drilling and routing steps to ensure the geometric accuracy and functionality of the PCB.

[0005] This invention discloses an optimized method for manufacturing a rotatable developable panel, which optimizes curvature constraints, drilling, and plate forming, specifically as follows:

[0006] During film design, the curved PCB is unfolded into a flat surface, and routing, via patterns, solder mask layers, and character layers are created on the flat surface. The outline of the curved PCB is provided by the customer. If the shape of the curved PCB is derived from the equation of a cylindrical surface... It is determined that the length of its unfolded diagram is 2πr1, and the width is z1, forming a rectangle; if the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z1 axis, and its plot be a graph with a radius of... A sector-shaped plane with an arc length of 2πr²; if the shape of a curved PCB is derived from the equation of a frustum. It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The fan-shaped annular plane;

[0007] Using the intersection of its outline as the origin of coordinates, the customer's 3D coordinates are transformed into 2D coordinates through the corresponding 3D-2D transformation formula, resulting in a D-code original containing the position, shape or size of holes, pads, and wires. Then, according to the process requirements, the D-code original is subjected to line or aperture compensation operations to form a working draft and delivered for film production.

[0008] Map the target drilling position onto the plot plane, and convert the coordinates in the hole diagram into 3D cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a drilling coordinate file; drill according to the path in the drilling coordinate file, move the drill bit to the target drilling position, align the hole position with the projection on the generatrix and start drilling, use a ball end mill or drill bit, optimize the cutting angle to adapt to the surface normal, and use low speed and high feed segmented pecking drill;

[0009] Based on the 3D model of the target surface, a CNC milling path file matching the curvature of the 3D tool is generated. The coordinates in the hole diagram are converted to cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a 3D tool path file. Then, the milling is performed according to the 3D tool path. The milling cutter moves to the starting point of the slot at the target slot position to start milling. The milling cutter always points to the projection of the hole position on the generatrix. Milling ends at the end point of the slot. Ball end mill or multi-axis linkage machining is used, and low speed and high feed segmented pecking drilling is adopted.

[0010] The coordinate 3D-2D transformation formula or the coordinate 2D-3D transformation formula are respectively:

[0011] A. If the shape of the curved panel PCB is derived from the equation of a cylindrical surface... It is determined that the length of its display diagram is 2πr1 and the width is z1, which is a rectangle.

[0012] Then we have:

[0013] Let X1, corresponding to the rotation angle θ, be the arc length, then we have:

[0014] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0015]

[0016] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0017]

[0018] B. If the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z2 axis, and its plot have a radius of... A sector-shaped plane with an arc length of 2πr²;

[0019] Then we have:

[0020] Let the desired new planar coordinate system be:

[0021]

[0022] and:

[0023]

[0024] Right now:

[0025]

[0026] Substituting the first and second equations from the conical surface equation (6) along with equation (9) into the new plane coordinate system (8), we obtain the new plane coordinate system as follows:

[0027]

[0028] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0029]

[0030] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0031]

[0032] C. If the shape of the curved panel PCB is derived from the equation of a frustum It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The sector-shaped annular plane; let O be the center of the bottom surface of the frustum, O' be the center of the top surface of the frustum, PM be the generatrix, and B be the endpoint of the frustum when the generatrix PM is rotated by an angle α from point M;

[0033] but:

[0034]

[0035] Solving for r from formula (14), we get:

[0036]

[0037] Right now:

[0038] Let α be the angle by which the generatrix PM rotates from point M to point B. Then we have:

[0039]

[0040] because:

[0041]

[0042] Right now:

[0043]

[0044] Therefore:

[0045]

[0046] Let the distance from point P to point M be ρ, then we have:

[0047]

[0048] Let the desired new planar coordinate system be:

[0049]

[0050] Substituting formulas (18) and (19) into the new plane coordinate system (20), we obtain the new plane coordinate system as follows:

[0051]

[0052] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0053]

[0054] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0055]

[0056] A curved support mold is used to fit the back of the curved PCB to ensure that the substrate does not collapse during drilling. At the same time, a removable rigid backplate is attached to the back of the curved PCB.

[0057] After adopting the technical solution of this invention, during the layout and routing, the customer's 3D coordinates are converted into 2D coordinates according to the 3D-2D transformation formula corresponding to the curved PCB shape, resulting in a D-code original containing the position, shape, or size of holes, pads, and conductors, thus achieving curvature adaptation for graphic transfer. Then, a curved support mold (contouring fixture) is used to fit the back of the curved PCB to ensure that the substrate does not collapse locally during drilling. At the same time, a temporary backplate is added to enhance local rigidity and achieve curvature constraint before drilling. The coordinates in the hole drawing are converted into cylindrical coordinates through the corresponding 2D-3D transformation formula to generate drilling coordinate files and 3D toolpath files. The drill bit or router bit always points to the projection of the hole position on the generatrix, ensuring the accuracy of the hole position and the curvature matching of the router board after rewinding. Low-speed, high-feed segmented pecking drilling is used to reduce heat accumulation and lateral force. Attached Figure Description

[0058] Figure 1 A cylindrical curved surface PCB and its layout;

[0059] Figure 2 A conical curved surface PCB and its layout;

[0060] Figure 3 A frustum-shaped curved PCB and its layout;

[0061] Figure 4 This is a schematic diagram illustrating how the present invention constrains the trajectory of the curvature center to make the curved PCB move up and down or rotate according to the expected target;

[0062] Figure 5 This is a schematic diagram of the drilling process of the present invention;

[0063] Figure 6 This is a schematic diagram of the forming process of the gong plate of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0065] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this application more complete and comprehensive, and to fully convey the concept of the exemplary embodiments to those skilled in the art.

[0066] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to provide a full understanding of the embodiments disclosed in this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of the disclosure of this application.

[0067] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or server that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0068] In this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or solution described as "exemplary" or "for example" in this application should not be construed as being better or more advantageous than other embodiments or solutions. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0069] The optimized method of this invention is explained in conjunction with the existing process for manufacturing developable PCBs:

[0070] 1. Implementation of curvature constraints

[0071] (1) Material selection and pretreatment:

[0072] Constructing a rigid-flexible composite structure: A flexible substrate is used in the curved area and FR-4 is used in the planar area. The curvature transition is achieved through a pressing process. The flexible substrate is selected from flexible materials such as polyimide (PI) or modified epoxy resin, which takes into account both flexibility and circuit stability.

[0073] Stress pre-release: By hot pressing or mechanical pre-bending, the substrate is pre-adapted to the target curvature, reducing deformation during subsequent processing.

[0074] (2) Curvature adaptation for graphic transfer:

[0075] Unfolding and Routing: Unfold the curved PCB into a flat surface, and perform routing, create via patterns, solder mask layers, and character layers on the flat surface, as well as obtain D-codes; the outline drawing of the curved PCB is provided by the customer in CAD or Pro / E format. If the shape of the curved PCB is derived from a cylindrical surface equation... If determined, then its unfolded diagram is a rectangle with a length of 2πr1 and a width of z1; if the shape of the curved panel PCB is derived from the equation of a conical surface... Given (ψ is the angle between the generatrix and the z2 axis), its development diagram has a radius of... A sector-shaped plane with an arc length of 2πr²; if the shape of a curved PCB is derived from the equation of a frustum. If confirmed, its display diagram will have an upper radius of... Lower radius is Angle is The fan-shaped annular plane.

[0076] The transformation process between 2D and 3D coordinates based on the shape of the curved PCB is as follows:

[0077] like Figure 1 As shown, if the shape of a curved panel PCB is derived from the equation of a cylindrical surface... It is determined that the length of its display diagram is 2πr1 and the width is z1, which is a rectangle.

[0078] Then we have:

[0079]

[0080] Let X1, corresponding to the rotation angle θ, be the arc length, then we have:

[0081]

[0082] The following 3D-to-2D coordinate transformation formula converts the customer's 3D coordinates to 2D coordinates, resulting in a D-code original containing the location, shape, or size of holes, pads, and wires:

[0083]

[0084] During drilling and milling, the coordinates of the 2D plane are mapped to the 3D surface using the following 2D-3D transformation formula:

[0085]

[0086] like Figure 2 As shown, if the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z2 axis, and its plot have a radius of... A sector-shaped plane with an arc length of 2πr²;

[0087] Then we have:

[0088]

[0089] Let the desired new planar coordinate system be:

[0090]

[0091] and:

[0092]

[0093] Right now:

[0094]

[0095] Substituting the first and second equations from the conical surface equation (6) along with equation (9) into the new plane coordinate system (8), we obtain the new plane coordinate system as follows:

[0096]

[0097] The following 3D-to-2D coordinate transformation formula converts the customer's 3D coordinates to 2D coordinates, resulting in a D-code original containing the location, shape, or size of holes, pads, and wires:

[0098]

[0099] During drilling and milling, the coordinates of the 2D plane are mapped to the 3D surface using the following 2D-3D transformation formula:

[0100]

[0101] like Figure 3 As shown, if the shape of the curved panel PCB is derived from the equation of a frustum... It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The annular plane of the sector; in the figure, O is the center of the bottom surface of the frustum, O' is the center of the top surface of the frustum, PM is the generatrix, and A and B are the two endpoints of the frustum when the generatrix is ​​rotated by an angle α from point M;

[0102] but:

[0103]

[0104] Solving for r from formula (14), we get:

[0105]

[0106] Right now:

[0107]

[0108] Let α be the angle by which the generatrix PM rotates from point M to point B. Then we have:

[0109]

[0110] because:

[0111]

[0112] Right now:

[0113]

[0114] Therefore:

[0115]

[0116] Let the distance from point P to point M be ρ, then we have:

[0117]

[0118] Let the desired new planar coordinate system be:

[0119]

[0120] Substituting formulas (18) and (19) into the new plane coordinate system (20), we obtain the new plane coordinate system as follows:

[0121]

[0122] The following 3D-to-2D coordinate transformation formula converts the customer's 3D coordinates to 2D coordinates, resulting in a D-code original containing the location, shape, or size of holes, pads, and wires:

[0123]

[0124] During drilling and milling, the coordinates of the 2D plane are mapped to the 3D surface using the following 2D-3D transformation formula:

[0125]

[0126] Dynamic exposure compensation: Using LDI (laser direct imaging) equipment, the exposure path is dynamically adjusted according to the planar graphic after the surface is unfolded to compensate for graphic distortion caused by curvature;

[0127] Segmented etching: Segmented etching is used for high curvature areas (such as reducing the concentration or time of the etching solution) to avoid stress concentration that could lead to copper layer peeling.

[0128] The optimization of this invention is as follows: When designing the film (taking a cylindrical surface as an example), the intersection of the outline of the plot, i.e., the lower right corner of the PCB board, is taken as the origin of the coordinate system. The 3D-2D transformation formula is then used:

[0129]

[0130] The client's 3D coordinates are converted into 2D coordinates to obtain a D-code original containing the position, shape, or size of holes, pads, and conductors. Then, according to the process requirements, a series of operations such as line or hole diameter compensation are performed on the D-code original to form a working draft, which is then delivered to the film supplier for film production.

[0131] 2. Drilling process optimization

[0132] (1) Curvature constraint before drilling:

[0133] The curvature constraint refers to constraining the trajectory of the curvature center, causing the curved PCB to move up and down or rotate according to the expected target during drilling and PCB forming (see...). Figure 4 If the curvature center trajectory is not constrained, oblique or crooked holes will be drilled, and the same applies to the drilled board. This invention uses a CNC-machined curved support mold (contouring fixture) to fit the back of the curved PCB, ensuring that there is no local collapse of the substrate during drilling. At the same time, a removable rigid back plate (such as acrylic or aluminum plate) is attached to the back of the curved PCB to enhance local rigidity by adding a temporary back plate.

[0134] The optimization of this invention is to attach a removable rigid backplate (such as acrylic or aluminum plate) to the back of the curved PCB to enhance local rigidity by adding a temporary backplate.

[0135] (2) Drilling optimization:

[0136] Mapping the target borehole location onto the plotting plane, i.e., through the 2D-3D coordinate transformation formula:

[0137]

[0138] The 2D coordinates (i.e., D-codes) in the hole diagram are converted into 3D cylindrical coordinates to generate a drilling coordinate file. Drilling is performed according to the path in the drilling coordinate file. The drill bit moves to the corresponding position according to the coordinate values ​​of the target drilling location. After the drill bit aligns with the projection of the hole position on the generatrix, drilling begins. The projection of the hole position on the generatrix is ​​the coordinate of the hole position on the z1 axis, which determines the drilling direction of the drill bit; for example... Figure 5As shown, the drill bit aligns with the projection of hole A on the curvature center trajectory and drills hole A (i.e., the drill bit points to the principal normal and drills hole A). Then, the drill bit is moved to hole B and aligned with the projection of hole B on the curvature center trajectory and drills hole B. Since the projections of holes C and D on the curvature center trajectory coincide and are higher than the projection of hole B, the drill press raises the curved PCB to the projection of hole C on the curvature center trajectory, and the drill bit rotates to hole C according to the drilling coordinate file. The drill bit aligns with the projection of hole C on the curvature center trajectory and drills hole C. Then, the drill bit is rotated to hole D and aligned with the projection of hole D on the curvature center trajectory and drills hole D.

[0139] The optimizations of this invention are as follows: the target drilling position is mapped onto the plotting plane to generate a drilling coordinate file, ensuring the accuracy of the hole position after rewinding; the mechanical drilling is improved by using a ball end mill or a custom drill bit, optimizing the cutting angle to adapt to the surface normal, and using low speed (<3000RPM), high feed segmented pecking drill to reduce heat accumulation and lateral force.

[0140] 3. Slot forming (cutting the outline of the slot)

[0141] (1) Curvature-adapted cutting path:

[0142] Based on the 3D model of the target surface, a 3D CNC milling path file matching the tool and curvature is generated, i.e., through the coordinate 2D-3D transformation formula:

[0143]

[0144] Convert the coordinates (i.e., D-code) in the hole diagram to cylindrical coordinates to generate a 3D toolpath file. Then, perform milling based on the 3D toolpath file. The milling cutter moves to the starting point of the slot according to the coordinate value of the target slot position to start milling. The milling cutter always points to the projection of the hole position on the generatrix. Milling ends at the end point of the slot. Use ball end mills or multi-axis linkage machining, and adopt low speed (<3000RPM), high feed segmented pecking drill to reduce heat accumulation and lateral force.

[0145] like Figure 6 As shown, after the 3D toolpath is obtained by transforming the 2D-3D coordinates using the following coordinate transformation formula, the 3D toolpath is rotated to the starting point A of the slot to begin 3D machining. The 3D toolpath always points to the projection of the hole position on the generatrix, and the machining ends at the ending point B of the slot.

[0146]

[0147] The optimization points of this invention are as follows: Based on the three-dimensional model of the target surface, a CNC milling path file matching the curvature of the 3D tool is generated. The coordinates in the hole diagram are converted into cylindrical coordinates through the corresponding coordinate 2D-3D transformation formula to generate a 3D tool path file. Then, the milling is performed according to the 3D tool path. The milling cutter moves to the starting point of the slot at the target slot position to start milling. The milling cutter always points to the projection of the hole position on the generatrix. Milling ends at the end point of the slot. Ball end mills or multi-axis linkage machining are used. Low speed and high feed segmented drilling is adopted. Ball end mills or multi-axis linkage machining are used to keep the cutting surface consistent with the surface normal and reduce heat accumulation and lateral force.

[0148] Laser cutting: Fiber laser cutting machines, combined with dynamic focusing systems, adapt to changes in surface height, enabling non-contact precision cutting. For flexible materials (such as PI), pulsed lasers are used to reduce the heat-affected zone.

[0149] (2) Cutting process control:

[0150] For thick plates or composite materials, layer milling (each layer depth ≤ 0.2 mm) is used to reduce the single cutting force. High-speed milling (spindle speed > 20,000 RPM) is performed with micro-lubrication (MQL) to reduce thermal deformation.

[0151] Pre-cut micro-stress relief grooves (0.1-0.3mm wide) on the outside of the cutting path to disperse the cutting stress.

[0152] (3) Tooling and Fixing:

[0153] A custom-designed vacuum adsorption platform with curved grooves ensures a perfect fit between the PCB and the tooling.

[0154] Flexible silicone pads are used to fill tiny gaps, enhancing the uniformity of adsorption;

[0155] Movable support pins (such as spring pin arrays) are installed on the back of the cutting area to provide local rigid support by dynamically following the tool position in real time.

[0156] 4. Key Quality Control Points

[0157] Curvature consistency inspection: Use a 3D scanner or laser profilometer to compare the deviation between the processed curved surface and the design model (must be <0.1mm);

[0158] Hole position accuracy verification: Check the hole position offset using an optical coordinate measuring machine (CMM) or a high-magnification microscope (allowable error ±0.05mm);

[0159] Electrical performance testing: Flying probe testing verifies the continuity of the circuit in high curvature areas, ensuring there are no microcracks or impedance abnormalities.

[0160] 5. Solutions for Special Scenarios

[0161] (1) Multi-curvature composite surface PCB:

[0162] Partitioned processing strategy: Divide the curved surface into multiple developable sub-regions (such as cylindrical surface + plane), perform graphic transfer and drilling separately, and finally splice them together to form the shape; embed metal reinforcing plates or increase copper thickness in the high curvature transition area to improve mechanical stability through local reinforcement structure.

[0163] (2) Dynamically bending PCBs (e.g., wearable devices):

[0164] The optimizations of this invention include: increasing fatigue life design, using arc-shaped traces (avoiding right-angle bends) to reduce bending stress concentration, and using electroplated soft gold (ENEPIG) as a surface treatment to enhance the fatigue resistance of solder joints.

[0165] Example 1

[0166] This invention discloses an optimized method for fabricating a PCB with a revolute developable surface, which optimizes curvature constraints, drilling, and PCB routing. Specifically:

[0167] During film design, the curved PCB is unfolded into a flat surface, and routing, via patterns, solder mask layers, and character layers are created on the flat surface. The outline of the curved PCB is provided by the customer. If the shape of the curved PCB is derived from the equation of a cylindrical surface... If determined, then its unfolded diagram is a rectangle with a length of 2πr1 and a width of z1; if the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z1 axis, then its development diagram has a radius of... A sector-shaped plane with an arc length of 2πr²; if the shape of a curved PCB is derived from the equation of a frustum. If confirmed, its display diagram will have an upper radius of... Lower radius is Angle is The fan-shaped annular plane;

[0168] Different curved PCB shapes result in different transformation formulas between 2D and 3D coordinates, specifically:

[0169] A. If the shape of the curved panel PCB is derived from the equation of a cylindrical surface... It is determined that the length of its display diagram is 2πr1 and the width is z1, which is a rectangle.

[0170] Then we have:

[0171]

[0172] Let X1, corresponding to the rotation angle θ, be the arc length, then we have:

[0173]

[0174] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0175]

[0176] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0177]

[0178] B. If the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z2 axis, and its plot have a radius of... A sector-shaped plane with an arc length of 2πr²;

[0179] Then we have:

[0180]

[0181] Let the desired new planar coordinate system be:

[0182]

[0183] and:

[0184]

[0185] Right now:

[0186]

[0187] Substituting the first and second equations from the conical surface equation (6) along with equation (9) into the new plane coordinate system (8), we obtain the new plane coordinate system as follows:

[0188]

[0189] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0190]

[0191] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0192]

[0193] C. If the shape of the curved panel PCB is derived from the equation of a frustum It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The sector-shaped annular plane; let O be the center of the bottom surface of the frustum, O' be the center of the top surface of the frustum, PM be the generatrix, and A and B be the two endpoints of the frustum when the generatrix PM is rotated by an angle α from point M.

[0194] but:

[0195]

[0196] Solving for r from formula (14), we get:

[0197]

[0198] Right now:

[0199]

[0200] Let α be the angle by which the generatrix PM rotates from point M to point B. Then we have:

[0201]

[0202] because:

[0203]

[0204] Right now:

[0205]

[0206] Therefore:

[0207]

[0208] Let the distance from point P to point M be ρ, then we have:

[0209]

[0210] Let the desired new planar coordinate system be:

[0211]

[0212] Substituting formulas (18) and (19) into the new plane coordinate system (20), we obtain the new plane coordinate system as follows:

[0213]

[0214] The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows:

[0215]

[0216] During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

[0217]

[0218] This invention uses a CNC-machined curved support mold to fit the back of a curved PCB, ensuring that the substrate does not collapse locally during drilling. At the same time, a removable rigid backplate is attached to the back of the curved PCB to enhance local rigidity by adding a temporary backplate.

[0219] Using the intersection of its outline as the origin of coordinates, the customer's 3D coordinates are transformed into 2D coordinates through the corresponding 3D-2D transformation formula to obtain the D-code original containing the position, shape or size of holes, pads, and wires. Then, according to the process requirements, the D-code original is subjected to line or aperture compensation operations to form a working draft, which is then delivered to produce film.

[0220] Map the target drilling position onto the plot plane, and convert the coordinates in the hole diagram into 3D cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a drilling coordinate file; drill according to the path in the drilling coordinate file, move the drill bit to the target drilling position, align the hole position with the projection on the generatrix and start drilling, use a ball end mill or drill bit, optimize the cutting angle to adapt to the surface normal, and use low speed and high feed segmented pecking drill;

[0221] Based on the 3D model of the target surface, a CNC milling path file matching the curvature of the 3D tool is generated. The coordinates in the hole diagram are converted to cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a 3D tool path file. Then, the milling is performed according to the 3D tool path. The milling cutter moves to the starting point of the slot at the target slot position to start milling. The milling cutter always points to the projection of the hole position on the generatrix. Milling ends at the end point of the slot. Ball end mill or multi-axis linkage machining is used, and low speed and high feed segmented pecking drilling is adopted.

[0222] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimized method for manufacturing a rotatable, developable panel, characterized in that, The curvature constraint, drilling, and milling process were optimized, specifically as follows: During film design, the curved PCB is unfolded into a flat surface, and routing, via patterns, solder mask layers, and character layers are created on the flat surface. The outline of the curved PCB is provided by the customer. If the shape of the curved PCB is derived from the equation of a cylindrical surface... It is determined that the length of its unfolded diagram is 2πr1, and the width is z1, forming a rectangle; if the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z1 axis, and its plot be a graph with a radius of... A sector-shaped plane with an arc length of 2πr²; if the shape of a curved PCB is derived from the equation of a frustum. It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The fan-shaped annular plane; Using the intersection of its outline as the origin of coordinates, the customer's 3D coordinates are transformed into 2D coordinates through the corresponding 3D-2D transformation formula, resulting in a D-code original containing the position, shape or size of holes, pads, and wires. Then, according to the process requirements, the D-code original is subjected to line or aperture compensation operations to form a working draft and delivered for film production. Map the target drilling position onto the plot plane, and convert the coordinates in the hole diagram into 3D cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a drilling coordinate file; drill according to the path in the drilling coordinate file, move the drill bit to the target drilling position, align the hole position with the projection on the generatrix and start drilling, use a ball end mill or drill bit, optimize the cutting angle to adapt to the surface normal, and use low speed and high feed segmented pecking drill; Based on the 3D model of the target surface, a CNC milling path file matching the curvature of the 3D tool is generated. The coordinates in the hole diagram are converted to cylindrical coordinates using the corresponding 2D-3D coordinate transformation formula to generate a 3D tool path file. Then, the milling is performed according to the 3D tool path. The milling cutter moves to the starting point of the slot at the target slot position to start milling. The milling cutter always points to the projection of the hole position on the generatrix. Milling ends at the end point of the slot. Ball end mill or multi-axis linkage machining is used, and low speed and high feed segmented pecking drilling is adopted.

2. The optimized method for manufacturing a rotatable and developable panel according to claim 1, characterized in that, The coordinate 3D-2D transformation formula or the coordinate 2D-3D transformation formula are respectively: A. If the shape of the curved panel PCB is derived from the equation of a cylindrical surface... It is determined that the length of its display diagram is 2πr1 and the width is z1, which is a rectangle. Then we have: Let X1, corresponding to the rotation angle θ, be the arc length, then we have: The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows: During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is: B. If the shape of the curved panel PCB is derived from the equation of a conical surface... Let ψ be the angle between the generatrix and the z2 axis, and its plot have a radius of... A sector-shaped plane with an arc length of 2πr²; Then we have: Let the desired new planar coordinate system be: and: Right now: Substituting the first and second equations from the conical surface equation (6) along with equation (9) into the new plane coordinate system (8), we obtain the new plane coordinate system as follows: The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows: During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is: C. If the shape of the curved panel PCB is derived from the equation of a frustum It is confirmed that its display diagram has an upper radius of... Lower radius is Angle is The sector-shaped annular plane; let O be the center of the bottom surface of the frustum, O' be the center of the top surface of the frustum, PM be the generatrix, and B be the endpoint of the frustum when the generatrix PM is rotated by an angle α from point M. but: Solving for r from formula (14), we get: Right now: Let α be the angle by which the generatrix PM rotates from point M to point B. Then we have: because: Right now: Therefore: Let the distance from point P to point M be ρ, then we have: Let the desired new planar coordinate system be: Substituting formulas (18) and (19) into the new plane coordinate system (20), we obtain the new plane coordinate system as follows: The 3D-to-2D transformation formula for converting a client's 3D coordinates to 2D coordinates, resulting in the original D-code containing the coordinates of holes, pads, wire positions, shapes, or sizes, is as follows: During drilling and milling, the 2D-3D transformation formula for mapping coordinates from a 2D plane to a 3D surface is:

3. The optimized method for manufacturing a rotatable and developable panel according to claim 1, characterized in that, A curved support mold is used to fit the back of the curved PCB to ensure that the substrate does not collapse during drilling. At the same time, a removable rigid backplate is attached to the back of the curved PCB.

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