Roller and method of designing the same

Abstract

The application discloses a roller and a design method thereof, and the method comprises the following steps: S1, a critical point L is obtained by integral for any one rotation surface of the roller n , the boundary of the rotation surface and the adjacent rotation surface is determined by extracting the critical point and the characteristic vector of the rotation surface, and the corresponding characteristic vector V is obtained after processing; S2, in the calculation process of the critical point, the adaptive factor of the initial phase of the rotation surface can be determined, and the initial position and the step length of the rotation surface can be determined; S3, the length of the clockwise or counterclockwise rotation surface arc is generated by continuously adding the number of continuation points through the determination of the initial position of the rotation surface and the change of the step length, and the arc has a non-equal length structure in the generation process by setting the change amount of the step length. The application adopts the judgment of the critical condition of the rotation surface, and the calculation complexity is reduced.

Description

Technical Field

[0001] This invention belongs to the technical field of cigarette manufacturing processes, and in particular relates to a roller and its design method. Background Technology

[0002] When cigarette factories manufacture cigarettes, cigarettes are considered qualified only if they pass through each production stage and meet the production process requirements. The brand name and vehicle number stamps on the surface of the cigarettes need to be sprayed evenly and appropriately onto the stamps through ink nozzles on the cigarette rolling machine, and then printed onto the surface of the cigarettes. The ink paste must be injected into the cigarette rolling machine by a special filling car.

[0003] Currently, domestic cigarette ink filling carts mainly employ a pneumatic pusher structure. Compressed air drives a pneumatic pump, which in turn moves a pusher to inject ink into the cigarette machine. During this process, the repeated back-and-forth movement of the pneumatic pump wears down the pusher and piston cup inside the filling cart. Over time, this causes instability in the pusher and piston cup's movement, affecting ink transfer. Furthermore, disassembling the pneumatic pump is extremely cumbersome, greatly inconveniencing the maintenance of the ink filling cart. The exterior and some internal views of the ink filling cart are shown below. Figure 1 , Figure 2 As shown. Summary of the Invention

[0004] To address the aforementioned technical problems in existing technologies, this invention provides a roller and its design method. Utilizing the roller's roller-type ink filling carriage, a local pressure difference is created within the filling body through a spiral propulsion mechanism, thereby extruding the ink from the cavity. For ink specifically designed for cigarette products, due to the ink's unique properties in viscosity, smoothness, and usage cycle, and the non-uniform length of the roller's rotating surface arc, this invention employs the determination of the rotating surface boundary conditions, reducing computational complexity; it also increases the overall structural balance of the arc-shaped rotating surface, enabling the roller to achieve lower resistance during rotation, while avoiding resonance during rotation, thus facilitating the optimization of the roller's rotating surface structure.

[0005] The technical solution adopted in this invention is:

[0006] A roller, characterized in that the roller is conical in shape, the conical shape includes multiple non-equal stainless steel turbine rotating surfaces, the multiple turbine rotating surfaces are coaxially stacked to form the roller, the roller body of the roller gradually decreases in size from left to right, ink paste enters from the large end side and flows out from the small end side by squeezing and rotating; the outer peripheral surface of each turbine rotating surface is an arc surface.

[0007] A roller design method, characterized by comprising the following steps:

[0008] S1. The critical point L is obtained by integration on any rotating surface of the roller.n The boundary between the rotation surface and adjacent rotation surfaces is determined by extracting the critical points and eigenvectors of the rotation surface, and then the corresponding eigenvector V is obtained after further processing.

[0009] S2. During the calculation of the critical point, the adaptive factor of the initial phase of the rotating surface can be determined, and the initial position and step size of the rotating surface can be determined.

[0010] S3. By determining the initial position of the rotating surface and changing the step size, the number of extension points is continuously added to generate the length of the clockwise or counterclockwise rotating surface arc. The arc has a non-uniform length structure during the generation process by setting the change amount of the step size. The cumulative value of the rotating surface arc is obtained by calculating the change amount of the step size of the rotating surface of the roller. Through continuous superposition, the facade structure of the non-uniform length arc rotating surface is finally obtained.

[0011] Furthermore, in step S1, each tangent point between the mutual contact of each rotating surface of the roller is defined as a critical point. These critical points can be regarded as points where the calculated values ​​converge or diverge when one rotating surface turns to another. The critical point L is calculated by integration over a certain rotating surface. n ,Right now

[0012] and

[0013] Where V1 and V2 represent two feature vectors, O n Let r represent the center of the plane of revolution. n Let θ represent the radius of the surface of revolution, θ represent the inclination of the surface of revolution relative to the horizontal, d represent the differential component, n represent the variable and n∈N, and N represents a natural number.

[0014] The rotating surface of the roller can be approximated by the critical point determined by the eigenvectors V1 and V2, and by the center O on the rotating surface. n and radius r n Together, they constitute the boundary conditions of a surface of revolution. Therefore, the boundaries of adjacent surfaces of revolution can be determined by extracting the critical points and eigenvectors of a surface of revolution.

[0015]

[0016] Where, ΔQ n-1 It is the adaptive factor for the initial phase, ΔQ end It is the adaptive factor for the terminal phase, ΔQ n-1 The larger the corresponding coordinate axis value, the greater ΔQ end The larger the corresponding coordinate axis value, the shorter the stretching step between the two, i.e., the arc of the rotation surface;

[0017] Then, using the standard equation of the plane, we can obtain:

[0018] (V1-L n ) 2 +(V2-L n ) 2 =r n 2 ,n∈N

[0019] Thus, the eigenvectors (V1, V2) of the surface of revolution are obtained. At this point, the eigenvectors V1, V2 of the surface of revolution and the center O are used to determine the eigenvectors V1, V2 of the surface of revolution. n and radius r n This allows us to determine the boundary conditions of the rotating surface, and so on, to determine the boundary conditions of all rotating surfaces in the roller.

[0020] Furthermore, in step S3, an arc-shaped iterative method is introduced during the shaping process of the rotating surface to optimize its structure. The shaping process of each arc-shaped rotating surface is considered as the accumulation of extension points on several infinitely extending tracks. The rotating surface is shaped by accumulating extension points, and the structure is optimized by setting constraints and predictions for the extension points. The stability of each extension point during the shaping process of the arc-shaped rotating surface is observed by the offset of the extension points. Furthermore, all subsequent extension points can be derived from the offset of the current extension point, thereby reducing the computational load. The specific steps are as follows:

[0021] ① Calculate the eigenvector (V1, V2) of the plane of revolution, and correspondingly transform it into the stable eigenvector (V3, V4) on the orbit, that is: V3 = f(V1, O n ,r n V4 = f(V2, O) n ,r n ), where f is the eigenvalue on the orbit, and together they constitute the characteristic stability space E on the orbit. 2 (V3,V4), where the spatial value is the variance;

[0022] ②, Based on the eigenvectors V3, V4 and O n r n The enclosed plane is an approximation of the initial plane of revolution. The nth extension point D is uniformly selected on this plane. n As the initial point for other extension points of the subsequent track, where D represents the extension point with values ​​taken in sequence;

[0023] ③ From this extension point D n To begin, we first calculate each arc segment using integration, i.e.:

[0024]

[0025] Where, d nW represents an infinitesimally small differential component with n as the variable. n The arcs represent the surface of revolution, and the endpoints of each arc segment form the initial points of a new arc segment.

[0026] ④ To keep the number of extension points on each arc roughly constant, the distance between the extension points on the arc needs to be checked. When the distance between two adjacent points is too small, one of the points should be removed. When the distance between two points is too large, a point should be inserted between the two points. When chaos occurs, that is, when some extension points that constitute one arc also constitute another arc, the arcs will become entangled with each other, causing the distance between the extension points to be too large or too small. In this case, the above operation needs to be repeated many times to keep the number of extension points on each arc constant and the distance between the extension points moderate.

[0027] The operation of removing an extension point is as follows:

[0028] if count(D n+1 D n )>D set

[0029] then delete D new

[0030] The operation of inserting an extension point is as follows:

[0031] if count(D n+1 D n ) <D set

[0032] then insert D new

[0033] ⑤ Treat the end point of the extension point on the obtained arc as the initial point on the new arc segment, and continue to repeat steps ① to ⑤. By continuously iterating the extension points to form a new surface of revolution, until the constraint value D of the orbital arc is satisfied. set Since no new extension points can be generated, a complete roller is eventually formed.

[0034] Furthermore, in step ⑤, in order to reduce interpolation error, it is necessary to estimate the number of extension points, thereby reducing the amount of computation; when estimating the number of extension points, it is assumed that there are already n extension points, that is, there is currently a set of extension points {D1, D2, ..., D...}. n-1 D n D n+1 ....}, n→+∞, as long as the extension point D is found. n+1 Calculate D n+1 With D n The step size between them, i.e., D 步长=||D n+1 -D n ||, then with the arc-shaped constraint value D set The comparison was made, and finally the step size change Δ was used. 步长 To estimate the number of extension points;

[0035] In order to find D n+1 We need to find D n+1 Mapping relationship point D' n+1 Since each extension point in the arc shape has a corresponding mapping point during the shaping process, this is to ensure that if an extension point is lost, it can be found again through the mapping point, i.e., D. n+1 =f(D' n+1 ),n∈N, where f represents the mapping relation and N represents the natural number;

[0036] After finding the extension point, the step size change Δ can be used to determine the extension point. 步长 To estimate the extension point, that is:

[0037] △ 步长 =D 步长 -D set

[0038]

[0039] Although in the above content, D set This has already been given as a reference value for the number of extension points in the system, but in practice it is still based on Δ. 步长 The change in the number of extension points is used to determine whether it is necessary to increase the number of extension points.

[0040] Furthermore, after estimating the number of extension points, the stability of each extension point needs to be predicted in advance using offset prediction. For a non-uniform length rotating surface, its shaping process can be regarded as an arc-shaped modeling process, and each extension point within it is a discrete factor in this discrete system. Therefore, the stability of the corresponding extension point can be determined by the offset of the extension point. The algorithm is as follows:

[0041] D n ∈{D1,D2,...,D n-1 D n D n+1 ,....},D1≠0,D n+1 =D n +1,n→+∞

[0042]

[0043] Where F represents the offset of the arc-shaped surface of revolution, and +∞ represents positive infinity; first, calculate the extension point D. n and Dn+1 The arc-shaped changes Δx and Δy along the x-axis and y-axis are then substituted into the formula to calculate the offset F. At this point, the extension point D is determined. n+1 Subsequent extension points can be derived using the offset F;

[0044] As can be seen from the above formula, during the shaping process of an arc-shaped rotating surface, if the previous extension point is in a stable or unstable state, the subsequent extension point will also maintain the same state as the previous extension point:

[0045] If the current extension point D n+1 It is in a stable state, and this extension point is the previous extension point D. n Based on the offset, the next extension point D is derived. n+2 Also according to the current extension point D n+1 If derived, the extension point D can be directly determined. n+2 It is a stable state, and there is no need to perform any further derivation or calculation.

[0046] If the current extension point D n+1 If it is an unstable state, then the arc-shaped surface of revolution shaped by the derived extension point is irregular.

[0047] Furthermore, in step S3, during the shaping process of the arc-shaped rotating surface, the number of extension points is continuously added by determining the initial position of the rotating surface and changing the step size, thereby generating the length of the clockwise or counterclockwise rotating surface arc. The step size variation is set to ensure that the arc has a non-uniform length structure during the generation process; let D... n For the nth extension point, that is:

[0048] D n ∈{D1,D2,...,D n-1 D n D n+1 ...}, n→+∞

[0049] N is a natural number, +∞ represents positive infinity, C is the step size change of the plane of revolution, and D... nx Let D be the set of extension points along the x-axis. ny Let be the set of extension points along the y-axis, then we have:

[0050]

[0051] Similarly, we have:

[0052]

[0053] Converting the expression into a conditional statement, we have:

[0054]

[0055] Similarly, D ny Conditional statements are similar to those described above, and are omitted here.

[0056] After the length of the arc is continuously superimposed on the arc-shaped surface of revolution, the set D of the extension points along the x-axis direction is... nx The set D of extension points along the y-axis ny Both of these values ​​would exceed the computer's maximum storage capacity. To ensure the validity of the cumulative value after the arc-shaped superposition, the following verification is required:

[0057] D less =(D nx |D set ) / (D n -D n-1 ) or D less =(D ny |D set ) / (D n -D n-1 ),n∈N,

[0058] Among them, D less D is the limit of the total number of extension points. set This is a system-limited value, based on the maximum number of bytes given by the modeling software; if D at this time less A positive value indicates that the number of extension points has not exceeded the arc limit and the accumulated data has not overflowed. Otherwise, a system error will occur and the number of extension points needs to be readjusted.

[0059] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0060] 1. This invention introduces the arc-shaped constraint method, which adopts the judgment of the boundary conditions of the rotating surface, reducing the computational complexity; it increases the overall balance of the arc-shaped rotating surface structure, so that the roller can obtain less resistance when it rotates, while avoiding the resonance generated during rotation, which facilitates the optimization of the roller rotating surface structure.

[0061] 2. This invention introduces an arc-shaped iterative method, which uses the accumulation of extension points to shape the rotating surface. By setting the constraints and predictions of the extension points, the structure of the rotating surface is optimized. The stability of each extension point during the shaping process of the arc-shaped rotating surface can be observed by the offset of the extension points. Furthermore, all subsequent extension points can be derived from the offset of the current extension point, thereby reducing the amount of computation. Attached Figure Description

[0062] Figure 1 It is the ink paste filling vehicle that uses a pneumatic push rod in the existing technology.

[0063] Figure 2 It is an injection body that uses a pneumatic push rod and a cup in the existing technology.

[0064] Figure 3 This is a schematic diagram of the roller structure of the present invention.

[0065] Figure 4 This invention is a three-dimensional roller structure constructed using the arc-shaped constraint method.

[0066] Figure 5 The present invention uses the arc-shaped constraint method to obtain the facade structure of a non-equal length arc-shaped rotating surface.

[0067] Figure 6 This describes the changes in the adaptive factors of the initial and final phases constructed using the arc-shaped constraint method in this invention.

[0068] Figure 7 This is a schematic diagram illustrating the parameterization of the rotating surface using the arc-shaped iteration method of the present invention.

[0069] Figure 8 This is a schematic diagram of the interpolation error generated during the adjustment of the extension point in this invention.

[0070] Figure 9 This is a schematic diagram of the rotating surfaces that are intertwined due to the initial estimation error of the present invention.

[0071] Figure 10 This is a schematic diagram of the tangential direction arrangement of the extension points of the rotating surface of the present invention.

[0072] Figure 11 This is a schematic diagram of the extension point shaping process in the stable state of the present invention.

[0073] Figure 12 This is a schematic diagram of the unsteady extension point shaping process of the present invention.

[0074] Figure 13 This is a schematic diagram comparing the shaping process of the extension point in stable and unstable states according to the present invention. Detailed Implementation

[0075] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0076] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0077] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments.

[0078] The optimization and precision of the overall roller structure are key to ensuring effective ink injection. The roller is composed of non-uniformly long stainless steel turbine rotating surfaces, with grooves between each rotating surface, and each blade edge of the roller is arc-shaped. Figure 4 As shown.

[0079] The optimization and precision of the overall roller structure described in this invention is based on the arc-shaped constraint method. This method has two main advantages: first, it uses the judgment of the boundary conditions of the rotating surface, reducing computational complexity; second, it increases the balance of the overall structure of the arc-shaped rotating surface, enabling the roller to obtain less resistance during self-rotation, while avoiding resonance generated during rotation, thus facilitating the optimization of the roller's rotating surface structure. The implementation steps are as follows:

[0080] ① The critical point is obtained by integration on any rotating surface of the roller. The boundary between the rotating surface and the adjacent rotating surface is determined by extracting the critical point and the eigenvector of the rotating surface. After further processing, the corresponding eigenvector is obtained.

[0081] ② In the process of calculating the critical point, the adaptive factor of the initial phase of the rotating surface can be determined, as well as the initial position and step size of the rotating surface.

[0082] ③ By determining the initial position of the rotating surface and changing the step size, the number of extension points is continuously added to generate the length of the clockwise or counterclockwise rotating surface arc. Furthermore, by setting the amount of change in the step size, the arc has a non-uniform length structure during the generation process.

[0083] The arc-shaped constraint method described in this invention can significantly improve the calculation speed while ensuring a certain level of accuracy. This method defines each tangent point between the mutual contact of each rotating surface of the roller as a critical point. These critical points can be seen as points where the calculated values ​​converge or diverge when one rotating surface turns to another. Therefore, by selecting any critical point for analysis and using its position as the initial position for integration, analysis results similar to those for the balance of rotating structures can be obtained. That is, by first integrating any rotating surface of the roller to obtain the critical point L... n By linearizing the vector, we can obtain the corresponding eigenvector V, and then use the eigenvector V to approximate the initial position of the surface of revolution.

[0084] Assume that the critical point L is calculated by integration on a certain rotating surface of the roller. n ,Right now:

[0085] and

[0086] Where V1 and V2 represent two feature vectors, O n Let r represent the center of the plane of revolution. nLet θ represent the radius of the surface of revolution, θ represent the inclination of the surface of revolution relative to the horizontal, d represent the differential component, n represent the variable, and N represent a natural number. For example... Figure 4 , Figure 5 As shown, it should be noted that Figure 4 The text only selects several critical points L between revolution plane 7 and revolution plane 6. n In fact, there are several critical points L between each plane of revolution. n .

[0087] As can be seen from the above, the rotating surface of the roller can be approximated by the critical point determined by the eigenvectors V1 and V2, and by the center O on the rotating surface. n and radius r n Together, they constitute the boundary conditions of a surface of revolution. Therefore, the boundaries of adjacent surfaces of revolution can be determined by extracting the critical points and eigenvectors of a surface of revolution.

[0088]

[0089] Then, using the standard equation of the plane, we can obtain:

[0090] (V1-L n ) 2 +(V 2 -L n ) 2 =r n 2 ,n∈N (3)

[0091] Thus, the eigenvectors (V1, V2) of the surface of revolution are obtained. At this point, the eigenvectors V1, V2 of the surface of revolution and the center O are used to determine the eigenvectors V1, V2 of the surface of revolution. n and radius r n By obtaining the two eigenvectors, the center, and the radius of the circle on the rotating surface, the boundary conditions of the rotating surface can be determined, thus significantly reducing the computational complexity.

[0092] At the critical point L n During the calculation, ΔQ n-1 It is the adaptive factor for the initial phase, ΔQ end It is the adaptive factor of the end phase. The first two in formula (2) are the adjustment calculations of the initial phase, that is, the determination of the initial position. The third formula is the adjustment of the end phase, that is, the determination of the step size. Therefore, it can be expanded to explain that at the critical point L n During the calculation, the range of position variation and the maximum step size have a significant impact on the shaping of the arc-shaped surface of revolution, and there is also a relationship between the two, ΔQ n-1 The larger the corresponding coordinate axis value, the greater ΔQend The larger the corresponding coordinate axis value, the shorter the stretching step (or arc length) between the two; conversely, the smaller the value, the shorter the stretching step (or arc length). n-1 The smaller, ΔQ end The less the difference, the longer the stretching step (or arc length) between the two. Furthermore, with the critical point L... n The more precise the summation of quantities, the range of positional changes, and the maximum distance of the step size, the more accurate the feature vectors V1, V2, and the center O. n radius r n The smaller the error of the resulting surface of revolution, the more likely it is to be extended in an arc shape. Simultaneously, the smaller the maximum step size, the shorter the single-step integral arc, the smaller the shaping bottleneck, and the better it reflects the detailed information in the shaping process. Figure 6 As shown.

[0093] During the shaping process of an arc-shaped surface of revolution, the number of extension points is continuously increased by determining the initial position of the surface of revolution and changing the step size, thereby generating the length of the clockwise or counterclockwise arc of revolution. Furthermore, by setting the step size variation, the arc has a non-uniform length structure during the generation process. Let D... n Let D be the nth extension point. n ∈{D1,D2,...,D n-1 D n D n+1 ...}, n∈N, and there are n extension points, C is the step size change of the rotation surface, D nx Let D be the set of extension points along the x-axis. ny Let be the set of extension points along the y-axis, then we have: Similarly, we have: Converting the expression into a conditional statement, we have:

[0094]

[0095] D ny Conditional statements are similar to those described above, and are omitted here.

[0096] After the length of the arc is continuously superimposed on the arc-shaped surface of revolution, the set D of the extension points along the x-axis direction is... nx The set D of extension points along the y-axis ny Both of these values ​​would exceed the computer's maximum storage capacity. To ensure the validity of the cumulative value after the arc-shaped superposition, the following verification is required:

[0097] D less =(D nx |D set ) / (D n -D n-1 ) or D less =(D ny |D set) / (D n -D n-1 ),n∈N,

[0098] Among them, D less D is the limit of the total number of extension points. set This is a system-limited value, based on the maximum number of bytes given by the modeling software; if D at this time less A positive value indicates that the number of extension points has not exceeded the arc limit and the accumulated data has not overflowed. Otherwise, a system error will occur and the number of extension points needs to be readjusted.

[0099] By calculating the step length change of the rotating surface of the roller, the cumulative value of the arc of the rotating surface is obtained. Through continuous superposition, the facade structure of the non-uniform arc rotating surface is finally obtained. In addition, due to the inclusion of limiting conditions in the design process, the rotating surface will not have the problem of system error caused by data overflow during the shaping process.

[0100] While structural errors can be avoided during the shaping process, a gap still exists compared to precise shaping. Therefore, an arc-shaped iterative method is introduced to optimize the structure of the rotating surface. Simply put, the shaping process of each arc-shaped rotating surface is viewed as the accumulation of extension points on several infinitely extending tracks. This method has two main advantages: First, it uses the accumulation of extension points to shape the rotating surface, optimizing the rotating surface structure by setting constraints and predictions for the extension points. Second, it observes the stability of each extension point during the shaping process of the arc-shaped rotating surface through the offset of the extension points, and can also deduce all subsequent extension points based on the offset of the current extension point, thereby reducing the computational load. The implementation steps are as follows:

[0101] ① Calculate the eigenvector (V1, V2) of the plane of revolution, and correspondingly transform it into the stable eigenvector (V3, V4) on the orbit, that is: V3 = f(V1, O n ,r n V4 = f(V2, O) n ,r n ), where f is the eigenvalue on the orbit, and together they constitute the characteristic stability space E on the orbit. 2 (V3,V4), where the spatial value is the variance.

[0102] ② In the eigenvectors V3, V4 and O n r n The enclosed plane is an approximation of the initial plane of revolution. The nth extension point D is uniformly selected on this plane. n As the initial point for other extension points of the subsequent orbit, where D represents the extension point whose values ​​are taken in sequence.

[0103] ③From this D nStarting from each extension point, first calculate an arc segment by integration, i.e.: Among them W n The arcs representing the surface of revolution, where the endpoints of each arc segment form the initial points of a new arc segment, such as... Figure 4 As shown, it should be noted that the figure only shows a segment of the arc of the rotating surface 5. In fact, each rotating surface is composed of multiple arc segments.

[0104] ④ To keep the number of extension points on each arc roughly constant, the distance between these points needs to be checked. If the distance between two adjacent points is too small, one of them should be removed; if the distance between two points is too large, a point should be inserted between them. When chaos occurs (where some extension points that make up one arc also make up another arc), the arcs will become entangled, causing the distance between extension points to be too large or too small. In this case, the above operation needs to be repeated multiple times to keep the number of extension points on each arc constant and the distance between them appropriate.

[0105] The operation of removing an extension point is as follows:

[0106] if count(D n+1 D n )>D set

[0107] then delete D new

[0108] The operation of inserting an extension point is as follows:

[0109] if count(D n+1 D n ) <D set

[0110] then insert D new

[0111] ⑤ Treat the end point of the extension point on the obtained arc as the initial point on the new arc segment, and continue to repeat steps ① to ⑤. By continuously iterating the extension points to form a new surface of revolution, the constraint value D of the orbital arc is satisfied. set However, it is impossible to generate new extension points, and its implementation process is as follows: Figure 8 As shown.

[0112] The aforementioned arc-shaped iteration method, from Figure 7As shown above, the figure approximates the initial surface of rotation as a plane. Five extension points are extracted from this plane: D1, D2, D3, D4, and D5. Extension point D3 is the initial point of the second surface of rotation. The figure shows that the second surface of rotation, after iteration through extension point D3 of the first surface of rotation, forms an arc L1. This arc L1, along with the feature vectors V3, V4, and O2, r2, forms a new plane, which is the second surface of rotation. Through this iterative process, a complete roller is finally formed.

[0113] The calculation error using this method mainly comes from two aspects. First, there is the interpolation error generated during the adjustment of the extension points. This is because when inserting a point between two extension points, it cannot be guaranteed that the point is exactly in the middle of the two points. Figure 8 As shown in the figure, the extension point D3 is not located between extension points D2 and D4, causing revolution surface 2 to be out of concentricity with revolution surface 1, and similarly causing revolution surface 3 to be out of concentricity. Secondly, there is an initial estimation error that occurs when initializing the extension points of the revolution surfaces. This is because, during the initialization of the extension points, it cannot be guaranteed that the extension point will be a unique initial point on the revolution surface; it may also be an initial point on another intertwined revolution surface. Figure 9 As shown, the extension point D3 is the initial point of both the rotation surface 2 and the rotation surface 3, resulting in the two rotation surfaces becoming entangled with each other.

[0114] To reduce interpolation errors, it's necessary to estimate the step size between each pair of points, which increases the computational load. When precise shaping of the revolution surface is required, more extension points are needed to reflect details. However, when only a rougher revolution surface needs to be shaped, maintaining the current number of extension points is sufficient. Therefore, it's necessary to estimate the number of extension points to reduce computation. Alternatively, extension points can be arranged along the tangent direction of the revolution surface to ensure a uniform distribution of the extension points forming the arc, thus reducing interpolation. However, while this method reduces interpolation, it alters the dynamic characteristics of the revolution surface, such as… Figure 10 As shown.

[0115] When estimating the number of extension points, it is assumed that there are already n extension points, that is, the current set of extension points is {D1, D2, ..., D...}. n-1 D n D n+1}, as long as the extension point D is found n+1 Calculate D n+1 With D n The step size between them, i.e., D 步长 =||D n+1 -D n ||, then with the arc-shaped constraint value D set The comparison was made, and finally the step size change Δ was used.步长 To estimate the number of extension points. In order to find D n+1 We need to find D n+1 Mapping relationship point D' n+1 Since each extension point in the arc shape has a corresponding mapping point during the shaping process, this is to ensure that if an extension point is lost, it can be found again through the mapping point, i.e., D. n+1 =f(D' n+1 ), n∈N, where f represents the mapping relationship and N represents the natural number.

[0116] After finding the extension point, the step size change Δ can be used to determine the extension point. 步长 To estimate the extension point, that is:

[0117] △ 步长 =D 步长 -D set

[0118]

[0119] Although in the above content, D set This has already been given as a reference value for the number of extension points in the system, but in practice it is still based on Δ. 步长 The change in the number of extension points is used to determine whether it is necessary to increase the number of extension points.

[0120] After estimating the number of extension points, offset prediction is then required. This can, to some extent, reduce the probability of intersecting rotational surfaces, i.e., reduce the possibility of rotational surfaces becoming entangled. Alternatively, the initial radius r of the rotational surface can be reduced. n To reduce the probability of mutual intersection, but at the same time r n It also cannot be too small, because r n If the value is too small, the overall shaping of the rotating surface cannot be achieved, ultimately leading to shaping failure of the roller or an unsatisfactory shaping effect. Therefore, to avoid r n To address the issue of excessively small values, this patent still employs offset prediction.

[0121] When using offset prediction, the stability of each extension point needs to be predicted in advance. This is because for a non-uniform length rotating surface, its shaping process can be viewed as an arc-shaped modeling process, and each extension point within it is a discrete factor in this discrete system. Therefore, the stability of the corresponding extension point can be determined by the offset of the extension point. The algorithm is as follows:

[0122] D n ∈{D1,D2,....D n-1 D n D n+1 ,....},D1≠0,D n+1 =Dn +1,n→+∞ (6)

[0123]

[0124] In the formula, F represents the offset of the arc-shaped rotating surface.

[0125] The stability of each extension point during the shaping of the arc-shaped rotating surface is observed by the offset of the extension point. Furthermore, as shown in the formula above, if the previous extension point is in a stable or unstable state during the shaping process, the subsequent extension point will also maintain the same state as the previous one. For example, if the current extension point D... n It is in a stable state, and this extension point is the previous extension point D. n-1 Based on the offset, the next extension point D is derived. n+1 Also according to the current extension point D n If derived, the extension point D can be directly determined. n+1 It is a stable state, and no further derivation or calculation is needed. For example, in the figure, first calculate the extension point D. n and D n+1 The arc-shaped changes Δx and Δy along the x-axis and y-axis are then substituted into the formula to calculate the offset F. At this point, the extension point D is determined. n+1 Subsequent extension points can be derived using the offset F. The advantage of this approach is that it eliminates the need for iterative calculations at each extension point; by obtaining the offsets of just two extension points, all subsequent extension points can be directly derived, thus reducing computational complexity. Figure 11 Examples of using offsets in the arc iteration method to observe the stable state of the extension point and Figure 12 An example of an unsteady state is given. Regarding the offset of the extension point, regardless of the current extension point D... n Whether a point is in a stable state or not, all subsequent extension points can be derived from the offset F. However, if the current extension point is in an unstable state, the arc-shaped surface of revolution shaped by the derived extension points will be irregular, such as... Figure 13 As shown in the figure, the extension point D n D n+1 D n+2 and D n+3 Although the step size is the same, the results after iteration show that the arc-shaped rotation surfaces shaped by the two are completely different in shape and structure. When the extension point is in an unstable state, the edge of the arc-shaped rotation surface is not smooth and the overall structure is irregular.

[0126] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A roller wheel, characterized in that The roller is conical, and the conical shape comprises a plurality of non-equal-length stainless steel turbine rotating surfaces which are coaxially stacked to form the roller, the roller body of the roller is sequentially reduced from left to right, and the ink paste enters from the large end side and flows out from the small end side through extrusion and rotation; the outer circumferential surface of each turbine rotating surface is an arc surface.

2. A method of designing a roller as claimed in claim 1, characterized in that The method comprises the following steps: S1, the critical point L is obtained by integration for any one rotation surface of the roller n The boundary of the rotation surface and the adjacent rotation surface is determined by extracting the critical point and the feature vector of the rotation surface, and the corresponding feature vector V is obtained after processing. S2, in the calculation process of the critical point, the adaptive factor of the initial phase of the rotating surface can be determined, and the initial position and step length of the rotating surface can be determined; S3, the length of the clockwise or counterclockwise rotating surface arc is generated by continuously stacking the number of continuation points through the determination of the initial position of the rotating surface and the change of the step length, and the arc has a non-equal-length structure in the generation process by setting the change amount of the step length; wherein, the cumulative value of the rotating surface arc is obtained by calculating the step length change amount of the rotating surface, and the non-equal-length arc rotating surface is finally obtained by continuously stacking.

3. The design method of the roller as claimed in claim 2, wherein, In step S1, each cutting point between the mutually intersecting each rotation surface of the roller is defined as a critical point, and these critical points can be considered as a point of convergence or divergence trend of the calculated value when one rotation surface turns to another rotation surface. The critical point L is calculated for a certain rotation surface using integration n i.e. wherein V1 and V2 represent two eigenvectors, respectively, O n denotes the center of a circle of a rotation surface, r n denotes the radius of the rotation surface, θ denotes the inclination of the rotation surface with respect to the horizontal, d denotes a differential, n denotes a variable, and N denotes a natural number; For the roller rotating surface can be approximated by the critical point determined by the eigenvector V1 and V2, and by the center of the rotating surface O n And the radius r n Together constitute a boundary condition of the rotating surface, so that the boundary of the adjacent rotating surface can be determined by extracting the critical point of a rotating surface and the eigenvector of the rotating surface, that is: Wherein, ΔQ n-1 is an adaptive factor of the initial phase, ΔQ end is an adaptive factor of the terminal phase, ΔQ n-1 The greater the corresponding coordinate axis value is, the shorter the step of stretching between the two, that is, the arc of the rotation surface is. end The greater the corresponding coordinate axis value is, the shorter the step of stretching between the two, that is, the arc of the rotation surface is. And then the standard equation of the plane can be obtained: Thus the eigenvectors (V1, V2) of the rotating surface are obtained, at this time the boundary conditions of the rotating surface can be determined through the eigenvectors V1, V2 of the rotating surface and the center O n and the radius r n of the circle, and so on, the boundary conditions of all rotating surfaces in the roller can be determined.

4. The design method of the roller as claimed in claim 2, wherein, In step S3, the arc iteration method is introduced in the shaping process of the rotating surface to optimize the structure of the rotating surface, and the shaping process of each arc rotating surface is regarded as the accumulation of continuation points on a plurality of infinitely extended tracks: the rotating surface is shaped by using the accumulation of continuation points, and the structure of the rotating surface is optimized by setting the limit conditions and estimation of the continuation points; whether each continuation point is stable in the shaping process of the arc rotating surface is observed by the offset amount of the continuation point, and all subsequent continuation points of the current continuation point can also be derived, thereby reducing the calculation amount; the specific steps are as follows: ①, calculate the eigenvectors of the rotating surface (V1, V2), correspondingly, transform into the stable eigenvectors on the orbit (V3, V4), that is: V3=f(V1, Or n ,r n ), V4=f(V2, Or n ,r n ), wherein f is the eigenvalue on the orbit, which together constitutes the eigenstable space E 2 (V3, V4) on the orbit, the space value is the variance value; ②, Based on the eigenvectors V3, V4 and O n r n The enclosed plane is an approximation of the initial plane of revolution. The nth extension point D is uniformly selected on this plane. n As the initial point for other extension points of the subsequent track, where D represents the extension point with values ​​taken in sequence; ③、From the extension point D n From the extension point D, first calculate a segment of arc by integration, namely: wherein represents a differential amount infinitely small with n as a variable, W n denotes an arc of a circle, the end point on each arc constituting an initial point on a new arc. (4) In order to keep the continuation points on each arc substantially constant, the distance between the continuation points on the arc needs to be checked, when the distance between the two adjacent points is too small, one of the two points needs to be removed, and when the distance between the two points is too large, a point needs to be inserted between the two points; when chaos occurs, that is, part of the continuation points on one arc also constitute another arc, the arcs will be intertwined with each other, causing the distance between the continuation points to be too large or too small, at this time, the above operation needs to be repeated multiple times to keep the number of continuation points on each arc constant and the distance between the continuation points moderate; The operation of removing a continuation point is: if count (D n+1 , D n ) > D set then delete D new The operation of inserting a continuation point is: if count (D n+1 , D n ) < D set then insert D new ⑤ Treat the end point of the extension point on the obtained arc as the initial point on the new arc segment, and continue to repeat the steps. ~ By iteratively extending the points to form new surfaces of rotation, the constraint value D of the orbital arc is satisfied. set Since no new extension points can be generated, a complete roller is eventually formed.

5. The design method of the roller as claimed in claim 4, wherein, In step ⑤, in order to reduce the interpolation error, the number of continuation points needs to be estimated, thereby reducing the calculation amount; when the number of continuation points is estimated, it is assumed that there are n continuation points at present, that is, there is a continuation point set , as long as the continuation point D n+1 is found n+1 , the step between D n and D set is calculated, compared with the arc limit value D 步长 , and finally the number of continuation points is estimated through the step change amount Δ n+1 . To find D n+1 , we need to find the mapping point D' n+1 of D n+1 . Since each extension point has a corresponding mapping point during the shaping process, we can find the extension point back through the mapping point if it is lost, that is , where f represents the mapping relationship and N represents a natural number. After the continuation point is found, the continuation point can be estimated by the step change amount Δ 步长 , that is: Although the above, D set A reference value for the number of continuation points has been given as a system, in fact, the amount of change in Δ 步长 is used to finally determine whether the number of continuation points needs to be increased.

6. The design method of the roller as claimed in claim 5, wherein, After estimating the number of continuation points, it is necessary to predict whether each continuation point is stable by using the offset amount prediction; for a non-equal-length rotating surface, its shaping process can be regarded as the modeling process of the arc, each continuation point in it is a discrete factor in the discrete system, so whether the corresponding continuation point is stable can be judged by the offset amount of the continuation point, and the algorithm is as follows: Wherein, F represents the offset of the arc-shaped rotating surface, +∞ represents positive infinity; first, the continuation point D n and D n+1 The arc-shaped variation amounts Δx and Δy of the x-axis and the y-axis are calculated, and then the variation amounts are substituted into the formula to calculate the offset F, and at this time, the continuation point D n+1 The subsequent continuation points can be derived through the offset F; From the above formula, it can be seen that in the shaping process of the arc rotating surface, if the previous continuation point is in a stable or unstable state, the next continuation point also maintains the same state as the previous continuation point: If the current continuation point D n+1 is stable, and the continuation point is the last continuation point D n derived according to the offset, then the next continuation point D n+2 is also derived according to the current continuation point D n+1 , then the continuation point D n+2 is stable without having to perform the corresponding derivation calculation again. If the current continuation point D n+1 is unstable, the arc-shaped rotating surface shaped by the derived continuation point is irregular.

7. The design method of the roller as claimed in claim 2, wherein, In step S3, when the arc-shaped rotating surface is continuously superimposed with the number of extension points in the shaping process, the length of the arc-shaped rotating surface is generated by the determination of the initial position of the rotating surface and the change of the step length, and the arc-shaped rotating surface has a non-equal length structure in the generation process by setting the step length change amount; let D n is the nth extension point, that is: N is a natural number, +∞ indicates a positive infinite, C is a step change amount of a rotation surface, D nx is a set of extension points in the x-axis direction, D ny is a set of extension points in the y-axis direction, and then the following is obtained: Similarly, we have: By converting the algorithm into a conditional statement, we have: define #D nx while D nx > 0 C = C + Math.pow(D, n-1) n , n-1) if C=C+1 and C>=1 then system.out.printIn(D x ) By analogy, D ny The same syntax is used to convert to conditional statements; After the length of the arc-shaped rotating surface is continuously stacked, the set D of the continuation points along the x-axis direction nx and the set D of the continuation points along the y-axis direction ny Both of them will exceed the maximum storage capacity of the computer. In order to ensure the effectiveness of the cumulative value after the arc-shaped stacking, the following verification needs to be done, that is: ， Where, D less is the limit value of the total number of extension points, D set is the system limit value, according to the maximum number of bytes given by the modeling software; if D less is a positive value, it means that the number of extension points does not exceed the arc limit value, and the accumulated value data does not overflow, otherwise, it will produce a system error, and the number of extension points needs to be adjusted.

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