Automatic generation method and system for hot runner system machining drawing

Abstract

The invention discloses a hot runner system machining drawing automatic generation method and system. The method comprises the following steps that a machining datum point P0 and a datum direction angle theta0 of a splitter plate are determined; setting expansion coefficients e of part positions on the upper and lower surfaces of the splitter plate; reading position coordinates Pn of parts on the upper and lower surfaces of the splitter plate based on P0 and direction angles theta n relative to theta 0; calculating the position coordinates Pn'of the parts on the upper and lower surfaces of the splitter plate after expansion based on P0; the Pn'is rotated by theta 0 relative to P0, the machining position coordinates Pn ''and the machining direction angle theta n' of the parts on the upper surface and the lower surface of the splitter plate are calculated, and the hot runner system machining drawing is generated accordingly The problems that in a traditional mode of manually drawing the hot runner system machining drawing, efficiency is low, and errors are prone to occurring in the drawing process are solved.

Description

Technical Field

[0001] The invention relates to the technical field of hot runner system processing diagram generation, and in particular to a method and system for automatically generating a hot runner system processing diagram. Background Art

[0002] As an important part of the injection mold, the core structure of the hot runner system usually includes the manifold and various parts installed on the upper and lower surfaces of the manifold. In the production and processing flow of the hot runner system, the drawing of the processing drawing is an indispensable link, which directly guides the subsequent production and manufacturing process. Traditionally, this drawing work relies on manual operation of the staff. They need to mark the specific position and direction of the manifold and its upper and lower surface parts on the drawing one by one according to the design requirements and part dimensions. However, with the continuous growth of production demand, manual drawing operations are not only inefficient and difficult to meet the needs of large-scale production, but also prone to errors in the drawing process, which in turn affects the accuracy and reliability of the processing drawings. Summary of the invention

[0003] In view of the above-mentioned defects, the present invention proposes a method and system for automatically generating hot runner system processing drawings, aiming to solve the problem that the traditional method of relying on manual drawing of hot runner system processing drawings is not only inefficient and difficult to meet the needs of large-scale production as production demand continues to grow, but also prone to errors in the drawing process, thereby affecting the accuracy and reliability of the processing drawings.

[0004] To achieve this object, the present invention adopts the following technical solutions:

[0005] A method for automatically generating a processing drawing of a hot runner system, wherein the hot runner system includes a manifold and parts on the upper and lower surfaces of the manifold, and comprises the following steps:

[0006] Step S1: Determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold;

[0007] Step S2: setting the expansion coefficient e of the parts position on the upper and lower surfaces of the manifold;

[0008] Step S3: Read the names of the parts on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer;

[0009] Step S4: Based on the expansion coefficient e of the parts on the upper and lower surfaces of the manifold and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n ');

[0010] Step S5: P n '(x n ',y n ') rotates θ0 relative to P0, and calculates the processing position coordinates P of the parts on the upper and lower surfaces of the manifold n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows:

[0011]

[0012] Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0;

[0013] Step S6: Calculate the machining direction angle θ of the parts on the upper and lower surfaces of the manifold n ', where θ n 'The specific calculation formula is as follows:

[0014] θ n '=θ n +θ0;

[0015] Step S7: According to P n ”(x n ”,y n ”) and θ n ', generate the hot runner system processing drawing.

[0016] Preferably, in step S2, the following sub-steps are specifically included: step S21: obtaining the expansion coefficient r of the manifold material; step S22: obtaining the difference ΔT between the hot runner system temperature and the hot runner system mold temperature; step S23: calculating the expansion coefficient e of the part position on the upper and lower surfaces of the manifold according to r and ΔT, and the specific calculation formula is as follows:

[0017] e=1-(r*ΔT).

[0018] Preferably, in step S4, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 n '(x n ',y n ')The specific calculation formula is as follows:

[0019]

[0020] Another aspect of the present application provides a system for automatically generating a hot runner system processing diagram, the system comprising:

[0021] A determination module is used to determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold;

[0022] A setting module, used to set the expansion coefficient e of the part position on the upper and lower surfaces of the manifold;

[0023] The reading module is used to read the part names on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer;

[0024] The first calculation module is used to calculate the expansion coefficient e of the parts on the upper and lower surfaces of the diverter plate and the position coordinates P of the parts on the upper and lower surfaces of the diverter plate based on P0. n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n ');

[0025] Rotating adjustment module, used to adjust P n '(x n ',y n ') rotated by θ0 relative to P0;

[0026] The second calculation module is used to calculate the processing position coordinates P of the parts on the upper and lower surfaces of the diverter plate n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows:

[0027]

[0028] Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0;

[0029] The third calculation module is used to calculate the processing direction angle θ of the parts on the upper and lower surfaces of the splitter platen ', where θ n 'The specific calculation formula is as follows:

[0030] θ n '=θ n +θ0;

[0031] Generate a module for n ”(x n ”,y n ”) and θ n ', generate the hot runner system processing drawing.

[0032] Preferably, the setting module includes: a first acquisition submodule, used to obtain the expansion coefficient r of the manifold material; a second acquisition submodule, used to obtain the difference ΔT between the hot runner system temperature and the hot runner system mold temperature; a first calculation submodule, used to calculate the expansion coefficient e of the part position on the upper and lower surfaces of the manifold based on r and ΔT, and the specific calculation formula is as follows: e=1-(r*ΔT).

[0033] Preferably, in the first calculation module, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 n '(x n ',y n ')The specific calculation formula is as follows:

[0034]

[0035] The technical solution provided by the embodiments of the present application may have the following beneficial effects:

[0036] In this solution, the processing position coordinates and processing direction angles of the parts on the upper and lower surfaces of the manifold are accurately calculated, and the hot runner system processing drawings are automatically generated based on them. Compared with relying on manual drawing of hot runner system processing drawings, this can not only improve the production efficiency of the hot runner system, but also reduce human errors in the drawing process, thereby improving the accuracy and reliability of the processing drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The invention is a flowchart of the steps of a method for automatically generating a hot runner system processing diagram. DETAILED DESCRIPTION

[0038] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0039] A method for automatically generating a processing drawing of a hot runner system, wherein the hot runner system includes a manifold and parts on the upper and lower surfaces of the manifold, and comprises the following steps:

[0040] Step S1: Determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold;

[0041] Step S2: setting the expansion coefficient e of the parts position on the upper and lower surfaces of the manifold;

[0042] Step S3: Read the names of the parts on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer;

[0043] Step S4: Based on the expansion coefficient e of the parts on the upper and lower surfaces of the manifold and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0 n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n ');

[0044] Step S5: P n '(x n ',y n ') rotates θ0 relative to P0, and calculates the processing position coordinates P of the parts on the upper and lower surfaces of the manifold n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows:

[0045]

[0046] Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0;

[0047] Step S6: Calculate the machining direction angle θ of the parts on the upper and lower surfaces of the manifold n ', where θ n 'The specific calculation formula is as follows:

[0048] θ n '=θ n +θ0;

[0049] Step S7: According to P n ”(x n ”,y n ”) and θ n ', generate the hot runner system processing drawing.

[0050] A method for automatically generating a hot runner system processing diagram in this solution, such as Figure 1 As shown, the first step is to determine the processing reference point P0 and the reference direction angle θ0 of the manifold. The processing reference point P0 is located on the reference direction straight line of the manifold. In this embodiment, by determining the processing reference point P0 and the reference direction angle θ0 of the manifold, it is helpful to ensure that the processing position and direction of the parts on the upper and lower surfaces of the manifold are determined relative to a fixed reference system. The second step is to set the expansion coefficient e of the position of the parts on the upper and lower surfaces of the manifold. In this embodiment, since the parts on the upper and lower surfaces of the manifold may change their position due to factors such as thermal expansion during the processing, setting the expansion coefficient e of the parts on the upper and lower surfaces of the manifold helps to ensure that the final processed part size meets the design requirements. Further explanation: the parts on the upper surface of the manifold include the main nozzle, cylinder, upper pad, manifold screws and temperature sensing device, etc., and the parts on the lower surface of the manifold include the center nail, hot nozzle, lower pad and positioning pin, etc. The third step is to read the part names on the upper and lower surfaces of the manifold, the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0 n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer. In this embodiment, by obtaining the names of the parts on the upper and lower surfaces of the diverter plate, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate based on P0 n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , which is conducive to the calculation of the processing position and direction of the parts on the upper and lower surfaces of the manifold. The fourth step is to calculate the expansion coefficient e of the parts on the upper and lower surfaces of the manifold based on P0 and the position coordinates P of the parts on the upper and lower surfaces of the manifold. n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n '), in this embodiment, the position coordinates P of the parts on the upper and lower surfaces of the manifold are calculated based on P0 by using the expansion coefficient e of the parts on the upper and lower surfaces of the manifold n (x n ,yn ) is corrected, taking into account the position changes of the parts on the upper and lower surfaces of the manifold due to factors such as thermal expansion during the processing, thereby improving the accuracy of subsequent processing. The fifth step is to n '(x n ',y n ') rotates θ0 relative to P0, and calculates the processing position coordinates P of the parts on the upper and lower surfaces of the manifold n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows: Wherein, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0. In this embodiment, in the actual processing of the hot runner system, the parts need to be rotated to a specific angle before processing. n '(x n ',y n ') Rotate according to θ0 to ensure that the parts can be correctly positioned and aligned during the actual processing. The sixth step is to calculate the processing direction angle θ of the parts on the upper and lower surfaces of the manifold n ', where θ n 'The specific calculation formula is as follows: θ n '=θ n +θ0, in this embodiment, by calculating the processing direction angle of the parts on the upper and lower surfaces of the manifold, it is beneficial to generate the subsequent hot runner system processing diagram. The seventh step is to calculate the processing direction angle of the parts on the upper and lower surfaces of the manifold according to P n ”(x n ”,y n ”) and θ n ', generate a hot runner system processing diagram. In this embodiment, by determining the processing position coordinates and processing direction angles of the parts on the upper and lower surfaces of the manifold, it is helpful to ensure that the parts are accurately positioned and in the correct direction during the processing.

[0051] In this solution, the processing position coordinates and processing direction angles of the parts on the upper and lower surfaces of the manifold are accurately calculated, and the hot runner system processing drawings are automatically generated based on them. Compared with relying on manual drawing of hot runner system processing drawings, this can not only improve the production efficiency of the hot runner system, but also reduce human errors in the drawing process, thereby improving the accuracy and reliability of the processing drawings.

[0052] Preferably, in step S2, the following sub-steps are specifically included: step S21: obtaining the expansion coefficient r of the manifold material; step S22: obtaining the difference ΔT between the hot runner system temperature and the hot runner system mold temperature; step S23: calculating the expansion coefficient e of the part position on the upper and lower surfaces of the manifold according to r and ΔT, and the specific calculation formula is as follows:

[0053] e=1-(r*ΔT).

[0054] Specifically, the hot runner system mold is a key tool for hot runner system injection molding. The various parts of the hot runner system will experience heating and expansion during the injection molding process, resulting in changes in the positions of the parts. Therefore, by calculating the expansion coefficient r of the manifold material and the difference ΔT between the hot runner system temperature and the hot runner system mold temperature, the expansion coefficient of the part position on the upper and lower surfaces of the manifold can be calculated, thereby further calculating the displacement of the parts on the upper and lower surfaces of the manifold due to thermal expansion during the injection molding process.

[0055] In one embodiment, when the material of the splitter plate is steel, the expansion coefficient r of the steel is 12*10 -6 When the difference ΔT between the hot runner system temperature and the hot runner system mold temperature is detected to be 200°C, the expansion coefficient e of the parts on the upper and lower surfaces of the manifold is 1-(12*10 -6 *200), which is 0.9976.

[0056] Preferably, in step S4, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 are n '(x n ',y n ')The specific calculation formula is as follows:

[0057]

[0058] In this embodiment, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 are calculated. n '(x n *e,y n *e), so that the position changes of the parts on the upper and lower surfaces of the manifold can be fully considered due to thermal expansion in the subsequent actual processing, thereby improving the accuracy of subsequent processing.

[0059] Another aspect of the present application provides a system for automatically generating a hot runner system processing diagram, the system comprising:

[0060] A determination module is used to determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold;

[0061] A setting module is used to set the expansion coefficient e of the part position on the upper and lower surfaces of the manifold;

[0062] The reading module is used to read the part names on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer;

[0063] The first calculation module is used to calculate the expansion coefficient e of the parts on the upper and lower surfaces of the diverter plate and the position coordinates P of the parts on the upper and lower surfaces of the diverter plate based on P0. n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n ');

[0064] Rotating adjustment module, used to adjust P n '(x n ',y n ') rotated by θ0 relative to P0;

[0065] The second calculation module is used to calculate the processing position coordinates P of the parts on the upper and lower surfaces of the diverter plate n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows:

[0066]

[0067] Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0;

[0068] The third calculation module is used to calculate the processing direction angle θ of the parts on the upper and lower surfaces of the splitter plate n ', where θ n 'The specific calculation formula is as follows:

[0069] θ n '=θ n +θ0;

[0070] Generate a module for n ”(x n ”,y n ”) and θ n', generate the hot runner system processing drawing.

[0071] The present solution is a hot runner system processing drawing automatic generation system, which realizes the automatic generation of the hot runner system processing drawing by the mutual cooperation of the determination module, the setting module, the reading module, the first calculation module, the rotation adjustment module, the second calculation module, the third calculation module and the generation module. In the present solution, the processing position coordinates and processing direction angles of the parts on the upper and lower surfaces of the manifold are accurately calculated, and the hot runner system processing drawing is automatically generated accordingly. Compared with relying on manual drawing of the hot runner system processing drawing, it can not only improve the production efficiency of the hot runner system, but also reduce human errors in the drawing process of the processing drawing, thereby improving the accuracy and reliability of the processing drawing.

[0072] Preferably, the setting module includes: a first acquisition submodule, used to obtain the expansion coefficient r of the manifold material; a second acquisition submodule, used to obtain the difference ΔT between the hot runner system temperature and the hot runner system mold temperature; a first calculation submodule, used to calculate the expansion coefficient e of the part position on the upper and lower surfaces of the manifold based on r and ΔT, and the specific calculation formula is as follows: e=1-(r*ΔT).

[0073] In this embodiment, the expansion coefficient of the parts position on the upper and lower surfaces of the diverter plate is calculated through the mutual cooperation of the first acquisition submodule, the second acquisition submodule and the first calculation submodule, so as to further calculate the displacement of the parts on the upper and lower surfaces of the diverter plate due to thermal expansion during the injection molding process.

[0074] Preferably, in the first calculation module, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 n '(x n ',y n ')The specific calculation formula is as follows:

[0075]

[0076] In this embodiment, the position coordinates P of the parts on the upper and lower surfaces of the diverter plate after expansion based on P0 are calculated. n '(x n *e,y n *e), so that the position changes of the parts on the upper and lower surfaces of the manifold can be fully considered due to thermal expansion in the subsequent actual processing, thereby improving the accuracy of subsequent processing.

[0077] In addition, each functional unit in each embodiment of the present invention may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0078] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for automatically generating a processing drawing of a hot runner system, wherein the hot runner system includes a manifold and parts on the upper and lower surfaces of the manifold, and wherein: The following steps are involved: Step S1: Determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold; Step S2: setting the expansion coefficient e of the parts position on the upper and lower surfaces of the manifold; Step S3: Read the names of the parts on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer; Step S4: Based on the expansion coefficient e of the position of the parts on the upper and lower surfaces of the manifold and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0 n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n '); Step S5: P n '(x n ',y n ') rotates θ0 relative to P0, and calculates the processing position coordinates P of the parts on the upper and lower surfaces of the manifold n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows: Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0; Step S6: Calculate the machining direction angle θ of the parts on the upper and lower surfaces of the manifold n ', where θ n 'The specific calculation formula is as follows: i n '=θ n +θ0; Step S7: According to P n ”(x n ”,y n ”) and θ n ', generate the hot runner system processing drawing.

2. The method for automatically generating a hot runner system processing diagram according to claim 1, characterized in that: In step S2, the following sub-steps are specifically included: Step S21: obtaining the expansion coefficient r of the material of the manifold; Step S22: obtaining a difference ΔT between the hot runner system temperature and the hot runner system mold temperature; Step S23: According to r and ΔT, the expansion coefficient e of the parts on the upper and lower surfaces of the manifold is calculated. The specific calculation formula is as follows: e=1-(r*ΔT).

3. The method for automatically generating a hot runner system processing diagram according to claim 1, characterized in that: In step S4, the position coordinates P of the parts on the upper and lower surfaces of the manifold are expanded based on P0. n '(x n ',y n ')The specific calculation formula is as follows:

4. A hot runner system processing diagram automatic generation system, using the hot runner system processing diagram automatic generation method according to any one of claims 1 to 3, characterized in that: The system comprises: A determination module is used to determine a processing reference point P0 and a reference direction angle θ0 of the manifold, wherein the processing reference point P0 is located on the reference direction straight line of the manifold; A setting module is used to set the expansion coefficient e of the part position on the upper and lower surfaces of the manifold; The reading module is used to read the part names on the upper and lower surfaces of the manifold, and the position coordinates P of the parts on the upper and lower surfaces of the manifold based on P0. n (x n ,y n ) and the direction angle θ of the parts on the upper and lower surfaces of the manifold relative to θ0 n , where n is a positive integer; The first calculation module is used to calculate the expansion coefficient e of the parts on the upper and lower surfaces of the diverter plate and the position coordinates P of the parts on the upper and lower surfaces of the diverter plate based on P0. n (x n ,y n ), calculate the position coordinates P of the parts on the upper and lower surfaces of the manifold after expansion based on P0 n '(x n ',y n '); Rotating adjustment module, used to adjust P n '(x n ',y n ') rotated by θ0 relative to P0; The second calculation module is used to calculate the processing position coordinates P of the parts on the upper and lower surfaces of the diverter plate n ”(x n ”,y n ”), where P n ”(x n ”,y n ”) The specific calculation formula is as follows: Among them, x0 represents the horizontal coordinate of the processing origin P0, and y0 represents the vertical coordinate of the processing origin P0; The third calculation module is used to calculate the processing direction angle θ of the parts on the upper and lower surfaces of the splitter plate n ', where θ n 'The specific calculation formula is as follows: i n '=θ n +θ0; Generate a module for n ”(x n ”,y n ”) and θ n ', generate the hot runner system processing drawing.

5. The hot runner system processing drawing automatic generation system according to claim 4, characterized in that: The setting module includes: The first acquisition submodule is used to obtain the expansion coefficient r of the material of the manifold; The second acquisition submodule is used to acquire the difference ΔT between the hot runner system temperature and the hot runner system mold temperature; The first calculation submodule is used to calculate the expansion coefficient e of the parts position on the upper and lower surfaces of the diverter plate according to r and ΔT. The specific calculation formula is as follows: e=1-(r*ΔT).

6. The hot runner system processing drawing automatic generation system according to claim 4, characterized in that: In the first calculation module, the position coordinates P of the parts on the upper and lower surfaces of the manifold are expanded based on P0. n '(x n ',y n ')The specific calculation formula is as follows:

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