A method for constructing an ODE-based plating equipment process tank weir flow head control model

Abstract

The present application relates to a kind of construction methods of weir flow head control model of electroplating equipment process tank based on ODE, belong to the technical field of semiconductor device surface treatment.The construction method includes step one: the calculation model of supply head of cleaning tank is constructed by Bernoulli equation in combination with pipeline loss;Step two: the flow calculation model of overflow weir is constructed, and the construction method of the flow calculation model of overflow weir includes: S1: the weir flow calculation model of top overflow weir is constructed;S2: the weir flow calculation model of middle circular overflow hole is constructed;S3: the flow calculation model of rectangular weir flow hole is constructed;S4: the flow calculation model at the outlet of water pump is constructed;Step three: the calculation model of pipeline loss is constructed, obtains entry boundary condition, and the minimum flow and lift required by water pump.The method can obtain minimum water pump flow and lift, and flow entry necessary condition, guarantee tank liquid level and flow stability, enhance the oil removal and cleaning effect to electronic device.

Description

Technical Field

[0001] This invention relates to a method for constructing a process tank weir flow head control model for electroplating equipment based on ODE, belonging to the field of semiconductor device surface treatment technology. Background Technology

[0002] In the field of semiconductor device manufacturing technology, when processing electronic devices using metal sheets as raw materials, punching or etching processes are typically used to shape the metal sheets into electronic devices of various required shapes. Then, surface treatment is performed on specific areas to obtain the corresponding electroplated products. To ensure the semiconductor devices possess reliable and excellent performance, the metal plating layer formed on the surface of the plated part needs to simultaneously possess high uniformity, high bonding strength, and excellent density. Therefore, thorough degreasing and cleaning are necessary before the electroplating process to ensure the device surface is sufficiently clean.

[0003] In the electroplating production of rolled metal sheets or lead frames, appropriate flow control models in degreasing and cleaning tanks not only ensure stable liquid levels and flow within the tanks but also enhance the degreasing and cleaning effects on electronic components. The weir head is a core parameter for regulating the flow state and liquid level in the process tanks. Improper control can lead to problems such as excessively high or low head, and turbulent fluctuations. Excessive head causes rapid overflow and violent surface fluctuations, while insufficient head results in inadequate replenishment and sluggish flow, directly disrupting the flow field balance within the tank. These problems cause persistently unstable liquid levels in the degreasing and cleaning tanks, and disordered fluctuations in the flow velocity and direction of the solution, preventing the formation of a uniform and stable circulating flow field. Turbulent flow fields prevent the continuous rinsing and removal of oil and impurities from the workpiece surface, leaving some stains in the substrate crevices and on the surface, significantly reducing the efficiency of degreasing and cleaning operations, and also leading to uneven cleaning in certain areas and an increase in cleaning dead zones.

[0004] Chinese patent document CN113239640A discloses an overflow weir design method for use in conjunction with a siphon-type water outlet channel. This design method enables high-flow pumping stations that do not have water level conditions in the outlet pool or outlet channel to also use a siphon-type water outlet channel. However, this method cannot control the weir head and cannot guarantee the stability of the liquid level and flow in the tank.

[0005] Chinese patent document CN120509343A discloses a method for predicting the pressure distribution along the flow path of a micro-spraying belt based on numerical simulation. Although it effectively reduces pressure loss, makes the pressure distribution along the flow path more uniform, and improves the uniformity of spraying, it mainly optimizes the head loss coefficient and pressure along the flow path, but does not optimize the relevant parameters of the weir head.

[0006] There is currently no effective solution to the aforementioned problems in the existing technology. Summary of the Invention

[0007] To address the aforementioned issues, this invention provides a method for constructing a process tank weir head control model for electroplating equipment based on ODE. By improving the weir head control, the degreasing and cleaning effects are enhanced, and the uniformity, bonding strength, and density of the coating are improved.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE, including... Step 1: Construct a calculation model for the water supply head of the cleaning tank by combining Bernoulli's equation with pipeline losses; Step 2: Constructing the flow calculation model for the overflow weir. The method for constructing the flow calculation model for the overflow weir includes: S1: Construct a calculation model for the flow rate of the top overflow weir; S2: Construct a weir flow calculation model for the central overflow orifice; S3: Construct a flow rate calculation model for a rectangular weir orifice; S4: Construct a flow calculation model at the water pump outlet; Step 3: Construct a calculation model for pipeline losses to obtain the flow head that satisfies the condition of the top weir. h The inlet boundary conditions at that time, and the minimum flow rate and head required by the water pump; Step 4: Based on the obtained minimum flow rate and head, adjust the opening of the inlet valve to control the inlet flow rate and keep the liquid level constant.

[0009] In one embodiment of the present invention, step one considers pipeline losses and constructs a modified Bernoulli equation, which is as follows: (2) In the formula, p The average pressure of the fluid in any cross-section of the pipeline system, expressed in Pa; v Let be the average flow velocity of the fluid in any cross-section of the pipeline system, in m / s; r The density of the fluid in any cross-section of the pipeline system, kg / m³ 3 ; H Let be the average height difference, in meters, of the fluid relative to a reference surface in any cross-section of the piping system; where the subscripts 0 and 1 represent any two different cross-sections in the piping system, respectively. H tl Let m be the pipe loss for streamlined particles between two different cross sections; g The acceleration due to gravity is m / s². 2 ; p / rg The pressure head of streamlined particles is expressed in meters (m).v 2 / 2g Let be the velocity head of the streamlined particle, in meters (m).

[0010] In one embodiment of the present invention, the flow rate of the top overflow weir is calculated in two ways depending on its thickness; When the thickness of the dam crest d >0.6 h At that time, the weir flow rate is calculated using an empirical formula: (8) When the thickness of the dam crest d ≤0.6 h At that time, the weir flow rate was calculated using Francis' semi-empirical formula: (9) In the formula, d Where is the thickness of the weir crest, in meters; and the weir flow coefficient is... C w ≈ 1.4 ~ 1.7, ; B The width of the broad-crested weir is in meters (m). Q top The flow rate at the top weir is m. 3 / s; h The head of the weir is measured in meters (m).

[0011] In one embodiment of the present invention, the formula for calculating the weir flow rate of the central overflow orifice is: (10) (11) In the formula, C v An empirical coefficient characterizing the effect of fluid viscosity on flow velocity, with a unit of 1; C c The contraction coefficient is expressed in units of 1; the orifice flow coefficient. C d = C v C c The unit is 1; A The overflow orifice area is m. 2 ; Q mid The flow rate at the central overflow orifice is m. 3 / s; v The average overflow velocity is expressed in m / s. H cLet be the height difference between the center of the hole and the free liquid surface, in meters (m).

[0012] In one embodiment of the present invention, the flow rate calculation formula for the rectangular weir orifice is as follows: (12) For the incremental flow d Q r In the interval ( H u , H d Integrating within the inner quadrant yields: (13) Considering the effect of the contraction section, the above equation can be simplified to (14) When the liquid level is within the rectangular weir orifice, for d Q r In the interval (0, ... H d Integrating within the interval yields... (15) In the formula, C d The orifice flow coefficient is... H d The height difference between the bottom of the orifice and the liquid surface, in meters (m). H u The height difference between the top of the orifice and the liquid surface, in meters (m). Q r The flow rate of the rectangular weir orifice is m. 3 / s; b The area increment d of the rectangle A Width, m; d h The area increment d of the rectangle A The height, in meters; h The area increment d of the rectangle A The height difference between the geometric center and the liquid surface, in meters (m); d A m is the area increment of the rectangle. 2 ;d Q r The area increment d of the rectangle A Incremental traffic within, m 3 / s.

[0013] In one embodiment of the present invention, the formula for calculating the flow rate at the water pump outlet is: (16) In the formula, N 1 represents the number of identical top overflow weirs in the system. N 2 represents the number of overflow holes in the middle section.N 3 represents the number of rectangular weir orifices in the system. Q 0 represents the water pump outlet flow rate, in m³ / s. 3 / s.

[0014] In one embodiment of the present invention, the formula for calculating the pipeline loss is: (18) In the formula, H tl For pipeline losses, m; M H represents the number of uniform straight pipes in the piping system. fl,i For the first i Friction loss along a uniform straight pipe, m; H ll,j For the first j The local loss of a local component, m.

[0015] In one embodiment of the present invention, the friction loss H fl The calculation formula is: (19) In the formula, l The friction factor of a straight pipe. l Let be the length of the straight pipe, in meters (m). d Let be the inner diameter of the straight pipe, in meters (m). g The acceleration due to gravity is m / s². 2 ; v The velocity of the liquid is expressed in m / s. The local loss H ll The calculation formula is: (twenty one) In the formula, v The average flow velocity across the cross section is given in m / s. g This is the local drag coefficient, with a unit of 1.

[0016] In one embodiment of the present invention, the head of the water pump H bump Should meet: (7) In the formula, H bump The head of the water pump is in meters (m).

[0017] In one embodiment of the present invention, the top weir head h The inlet boundary conditions are: (17) (26) In the formula, l i For the first i The friction coefficient of a uniform straight pipe, in units of 1; l i For the first i The length of a uniform straight pipe, in meters; d i For the first i The inner diameter of a uniform straight pipe, in meters; v i For the first i The average flow velocity in a uniform straight pipe, m / s; v j For the first j Local resistance coefficient of individual components g i The average flow velocity of the corresponding cross section, in m / s.

[0018] The beneficial effects of this invention are: The present invention provides a method for constructing a process tank weir flow head control model for electroplating equipment based on ODE, which has the following advantages: 1. The present invention provides a method for constructing a process tank weir head control model for electroplating equipment based on ODE. By combining classical computational fluid dynamics theory with empirical formulas for overflow weirs of different shapes, an engineering design model for controlling the weir head is established under the conditions of specified pipeline system, pump flow rate and head. This model can predict friction loss and local loss in the pipeline system, and determine the flow rate of the central circular overflow hole and the top weir head and flow rate in the tank. Based on the obtained flow rate, the opening of the inlet valve is adjusted to control the inlet flow rate, so that the liquid level remains constant, thereby ensuring the stability of the liquid level and flow in the tank and enhancing the degreasing and cleaning effect on electronic devices.

[0019] 2. This construction method can determine the pump flow rate and head required to achieve the expected target under the given pipeline system and weir head conditions, thereby reducing operating energy consumption, saving energy and increasing efficiency, optimizing equipment selection, reducing equipment size, ensuring stable water replenishment, ensuring smooth pipeline drainage without additional impact, stabilizing the flow field and liquid level, and thus improving the cleaning and oil removal effect. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 A schematic diagram of the top overflow weir provided by the present invention; Figure 2 This is a schematic diagram of the central circular overflow hole provided by the present invention; Figure 3 This is a schematic diagram of the rectangular weir orifice provided by the present invention; Figure 4 A schematic diagram showing the relative positions of the top overflow weir, the middle circular overflow hole, and the rectangular weir orifice provided by the present invention; Figure 5 This is a schematic diagram of the structure of the process tank of the electroplating equipment provided by the present invention; In the diagram: 1. Water pump outlet; 2. Local component; 3. First equal-section straight pipe; 4. Tee; 5. Single-slot equal-section straight pipe; 6. Elbow; 7. Second equal-section straight pipe; 8. Inner tank; 9. First cross-section; 10. Second cross-section; 11. Liquid surface; 12. Circular overflow hole; 13. Waste discharge port; 14. Rectangular weir orifice; 15. Top overflow weir; 16. Cleaning tank; 17. Support. Detailed Implementation

[0022] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. The terms "first position" and "second position" refer to two different positions.

[0024] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections or detachable connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal connections between two components. Those skilled in the art can understand the specific meaning of these terms in this invention based on the specific circumstances.

[0025] This invention provides a method for constructing a process tank weir head control model for electroplating equipment based on ODE (Ordinary Differential Equation). By improving the weir head control and combining it with an engineering design model for process tank weir head control in electroplating equipment, the degreasing and cleaning effects are enhanced, and the uniformity, bonding strength, and density of the coating are improved.

[0026] like Figure 1 to Figure 5 As shown, in some embodiments, the electroplating equipment process tank includes a support 17, on which a cleaning tank 16 is installed, and an inner tank 8 is installed inside the cleaning tank 16. A water pump is installed below the support 17, and one end of the water pump is connected to a water pump outlet 1. On the side of the water pump outlet 1 away from the water pump, a partial component 2, a first equal-section straight pipe 3, and a reducing tee 4 are sequentially connected. Single-tank equal-section straight pipes 5 are symmetrically installed on both sides of the reducing tee 4. An elbow 6 is connected to one side of the single-tank equal-section straight pipe 5. The elbow 6 passes through the cleaning tank 16 and is connected to the inner tank 8 through a second equal-section straight pipe 7. The top of the inner tank 8 is a top overflow weir 15, and its side is provided with a circular overflow hole 12 and a rectangular weir flow hole 14. A waste discharge port 13 is provided below the cleaning tank 16. A liquid surface 11 is formed at the top of the liquid in the inner tank 8, and the top overflow weir 15 includes a first cross-section 9 and a second cross-section 10.

[0027] Optionally, in this embodiment, the partial component 2 is a flange, which is connected to the water pump outlet 1.

[0028] Based on the above-mentioned electroplating equipment process tank, a method for constructing a weir flow head control model is provided. In the formula calculations involved in this method, standard physical units are used, that is, the unit of length is m and the unit of volume is m. 3 The unit of flow rate is m. 3 The pressure unit is Pa (Pa), and its construction method includes the following steps: Step 1: Calculate the water head supplied to the cleaning tank.

[0029] For an ideal fluid, neglecting pipe losses, and taking the horizontal plane where the pump outlet 1 is located as the reference plane, Bernoulli's equation can be expressed as follows: (1) In the formula, p The average pressure of the fluid in any cross-section of the pipeline system, expressed in Pa; v Let be the average flow velocity of the fluid in any cross-section of the pipeline system, in m / s; r The density of the fluid in any cross-section of the pipeline system, kg / m³ 3 ; g The acceleration due to gravity is m / s². 2 ; HLet be the average height difference, in meters, of the fluid relative to a reference surface in any cross-section of the piping system; where the subscripts 0 and 1 represent any two different cross-sections in the piping system, respectively. C is an undetermined constant.

[0030] However, considering pipeline losses in engineering applications, equation (1) can be modified as follows: (2) In the formula, H tl The pipe loss for streamlined particles between two different cross sections, m; in engineering applications, p / rg The pressure head of streamlined particles is expressed in meters (m). v 2 / 2g Let be the velocity head of the streamlined particle, in meters (m).

[0031] According to the law of conservation of mass, the flow rates at any given time for two different cross-sections... Q Equal, that is (3) From equation (3), we can obtain (4) In the formula, A 0、 A 1 represents the area of ​​two different cross-sections, in m. 2 ; Q 0、 Q 1 represents the flow rate at two different cross-sections, in m. 3 / s; coefficient of cross-sectional contraction C c = A 1 / A 0. Combining equations (2) and (4), the pressure across the cross section can be obtained. p Formula for calculating 1 (5) Step 2: Calculate the flow rate of the overflow weir.

[0032] S1: Calculation of the flow rate of the top overflow weir.

[0033] like Figure 1 As shown, when considering the application of an overflow weir at the top of the cleaning tank, the water flow needs to continue rising after passing the horizontal plane of the top overflow weir 15, until it exceeds the horizontal plane of the top overflow weir 15 by a small distance. h Without loss of generality, the top overflow weir 15 can be raised further. hThe cross sections after the water head are denoted as the first cross section 9 and the second cross section 10, respectively. The average flow velocity and pressure of the first cross section 9 can be calculated according to equations (4) and (5), respectively.

[0034] Assuming the weir head h Small enough (e.g.) h (≈5~10mm) and occurs within a very short time, with some streamlines in the liquid surface rising. h During the process, the outward diffusion in the horizontal direction due to the lack of wall constraints is ignored, thus assuming that the average horizontal velocity of this portion of the streamlines is zero during the upward flow. This is done upon reaching the weir head. h At a given moment, the average velocity of the corresponding streamlines in the vertical direction is zero, and the pressure head and velocity head are all converted into position head and pipe loss head. Furthermore, the interface between the streamlines and air at the weir is in an unstable equilibrium state. Although the horizontal momentum is zero, according to the law of conservation of mass, the weir head is disturbed by the continuous upward flow of subsequent water. In the absence of wall constraints, the weir head generates a small horizontal flow, which continues to flow under gravity and forms a weir flow.

[0035] The horizontal plane where the water pump outlet 1 is located is selected as the reference plane, that is, the cross section with subscript 0. Bernoulli's modified equation (2) is established for the reference plane, the first cross section 9 and the second cross section 10. (6) It is easy to know that the head of the water pump H bump Should meet (7) For an ideal broad-crested dam with a horizontal crest and a relatively large thickness (thickness...) d >0.6 h The water flow forms a critical flow at the crest of the weir, with streamlines that are approximately parallel. The weir flow rate can be calculated using empirical formulas. (8) In the formula, d Where is the thickness of the weir crest, in meters; and the weir flow coefficient is... C w ≈1.4~1.7, ; B The width of the broad-crested weir is in meters (m). Q top The flow rate at the top weir is m. 3 / s; h The head of the weir is measured in meters (m).

[0036] For rectangular sharp-flange weirs with very thin crests, the Francis Formula can be used to calculate the weir flow rate. When the weir crest width is similar to the channel width, the Francis Formula for weirs without lateral contraction can be used, i.e. (9) In this case, the energy described in formula (6) is entirely provided by the water pump. When it flows through the pipeline system to the second cross section 10, it is all converted into pipeline loss energy and gravitational potential energy.

[0037] S2: Calculation of weir flow rate at the central overflow orifice.

[0038] like Figure 2 As shown, when considering the application of tiny overflow holes inside the water tank, Torricelli's empirical formula can be used to estimate the average overflow velocity within the overflow hole. v : (10) In the formula, H c The height difference between the center of the hole and the free liquid surface is expressed in meters (m). C v An empirical coefficient characterizing the effect of fluid viscosity on flow velocity is used, depending on the orifice shape. C v ≈0.95~0.99, unit is 1; v The average overflow velocity is expressed in m / s.

[0039] Considering the constriction effect, the contraction section is smaller than the actual orifice area, and the contraction coefficient... C c ≈0.61~0.64, unit is 1. Flow rate at the central circular overflow orifice. Q mid An empirical formula can be used: (11) In the formula, the orifice flow coefficient C d = C v C c The unit is 1; A The overflow orifice area is m. 2 .

[0040] S3: Calculation of flow rate through rectangular weir orifice.

[0041] like Figure 3 As shown, when considering the application of rectangular weir orifices, equation (11) is no longer applicable due to the large orifice area. The increase in rectangular area at the orifice is d.A = b d h Incremental flow d Q r for: (12) In the formula, d A m is the area increment of the rectangle. 2 ;d Q r The area increment d of the rectangle A Incremental traffic within, m 3 / s; b The area increment d of the rectangle A Width, m; d h The area increment d of the rectangle A The height, in meters; h The area increment d of the rectangle A The height difference between the geometric center and the liquid surface, in meters (m).

[0042] For equation (12) in the interval ( H u , H d Integrating within the interval yields... (13) In the formula, H d The height difference between the bottom of the orifice and the liquid surface, in meters (m). H u The height difference between the top of the orifice and the liquid surface, in meters (m). Q r The flow rate of the rectangular weir orifice is m. 3 / s.

[0043] Considering the effect of the contraction section, the above equation can be simplified to (14) When the liquid level is within the rectangular weir orifice, for d Q r In the interval (0, ... H d Integrating within the interval yields... (15) In the formula, the orifice flow coefficient C d It can be determined based on commonly used typical flow coefficients, as shown in Table 1.

[0044] Table 1 Typical Flow Coefficients

[0045] S4: Calculation of water pump outlet flow rate.

[0046] According to the law of conservation of mass, we can conclude that: (16) In the formula, N 1~ N 3 represents the number of identical top overflow weirs 15, central circular overflow orifices 12, and rectangular weir orifices 14 in the system, respectively. Q The outflow of the system at any given time is equal to the inflow (i.e., the pump outlet flow rate). Q 0), m 3 / s. Substituting equations (3), (8), (11), and (15) into equation (16) yields (17) Step 3: Calculation of pipeline losses.

[0047] Typically, pipeline losses H tl (Total head loss) is determined by the head loss along the route, H. fl (frictional head loss) and local loss H ll The loss consists of two types: (local head loss) and (local head loss). It is assumed that every two uniform straight pipe sections in the pipeline system are connected by local components. (18) In the formula, M H represents the number of straight pipes with uniform cross-section in the piping system. fl,i For the first i Friction loss along the length of a straight pipe with uniform cross-section, m; H ll,j For the first j The local loss of a local component, m.

[0048] In engineering, the Darcy-Weisbach formula is often used to calculate friction loss H. fl ,Right now (19) In the formula, l The friction factor of a straight pipe. l Let be the length of the straight pipe, in meters (m). d Let be the inner diameter of the straight pipe, in meters (m). g The acceleration due to gravity is m / s². 2 ; v Let be the liquid flow velocity, in m / s. l The Reynolds number is determined by the fluid flow regime and pipe wall roughness. In pipe flow fields, it is often determined by the Reynolds number. Re = vd / u ( uThe flow regime is determined by the kinematic viscosity of the fluid. When the flow field is laminar ( Re ≤ 2320), the flow is stable. l = 64 / Re (Hagen-Poiseuille formula); when the flow field is turbulent ( Re >2320), complex flow regime, l and Re Relative roughness of pipe wall ( e / d , e This is related to the absolute roughness of the pipe wall and needs to be found using a Moody Chart or calculated using empirical formulas. For smooth straight pipes (new steel pipes)... e ≈ 10 ~ 15 μm or plastic tube e (≈ 0.8 μm), the Brahius formula and the Schifflinson formula can be used, i.e. (20) Local loss H ll This is due to concentrated losses caused by abrupt changes in the flow field. When fluid flows through local components of a pipeline (such as elbows, valves, reducing tees, inlets / outlets), abrupt changes in the flow field (such as cross-sectional contraction / expansion, or changes in flow direction) generate eddies and separation, resulting in energy loss. In engineering, this is often measured using the local drag coefficient. g To quantify local loss, i.e. (twenty one) In the formula, v The value is the average flow velocity across the downstream cross section of the relevant component, in m / s. g The values ​​are mainly determined experimentally, and can be found in engineering manuals for common components. g value.

[0049] For example, a 90° elbow g ≈ 0.7~1.0; Fully open gate valve g ≈ 0.17. At components with a suddenly enlarged cross-section, an empirical coefficient needs to be introduced to account for actual turbulent flow. g It can be represented as (twenty two) In the formula, A 0 and A 1 represents the area of ​​the front and rear cross sections, respectively, in m. 2 ; k ζ The flow velocity in equation (21) is an empirical coefficient (usually taken as 0.5~1.0). v The average flow velocity at the upstream small cross-section (m / s). For components where the cross-section suddenly narrows, the contraction coefficient (…). Cc = A 1 / A The commonly used experimental values ​​of 0) are shown in Table 2, and the flow rate in equation (21) is... v The average flow velocity is the velocity at the downstream small cross-section.

[0050] Table 2 Empirical values ​​of local resistance coefficient

[0051] When the fluid flows through the first m When dealing with a uniform straight pipe, substituting equations (18), (19), and (21) into Bernoulli's equation (2) and the mass conservation equation (4) yields the following results: (twenty three) (twenty four) In the formula, p m For the first m Pressure at the end of a straight pipe with uniform cross-section, Pa; v m For the first m Average flow velocity in a straight pipe with uniform cross-section, m / s; l i For the first i The friction coefficient of a straight pipe with uniform cross-section, in units of 1; l i For the first i The length of a straight pipe with uniform cross-section, in meters; d i For the first i The inner diameter of a straight pipe with uniform cross-section, in meters; v i For the first i Average flow velocity in a straight pipe with uniform cross-section, m / s; v j For the first j Local resistance coefficient of individual components g i The corresponding average flow velocity of the upstream or downstream pipeline, A m For the first m The cross-sectional area of ​​a straight tube with uniform cross-section, m 2 ; H m For the first m The potential head of a straight pipe with uniform cross-section at its end, in meters; C c,m is the shrinkage coefficient of the m-th straight pipe with uniform cross-section, in units of 1.

[0052] Based on equations (23) and (24), the average flow velocity, pressure, friction loss, and local losses in each uniform straight pipe section of the system can be calculated sequentially. Substituting these values ​​into equation (18) yields the total pipeline loss of the system. H tl for (25) Substituting equation (25) into equation (6) yields (26) Equations (17) and (26) are used to satisfy the top weir flow head as follows: h The necessary inlet boundary conditions, i.e., when the pump outputs pressure-flow rate ( p 0- v 0) When condition (26) is satisfied, the head of the top weir can reach h Considering the pump performance curve parameters, the minimum flow rate and head required by the pump can be obtained according to equations (16) and (7).

[0053] Step 4: Obtain the required head of the top weir. h After determining the necessary inlet boundary conditions, as well as the minimum flow rate and head required by the water pump, the opening of the inlet valve is adjusted according to the obtained flow rate to control the inlet flow rate and keep the liquid level constant, thereby ensuring the stability of the liquid level and flow in the tank and enhancing the degreasing and cleaning effect on electronic devices.

[0054] Example 1 like Figure 5 As shown, in a certain cleaning tank, the inner diameter of the water pump outlet 1 is... f in = 50 mm, simultaneously supplying two identical inner tanks 8. Since the water flows outwards and downwards along the single-sided cylindrical surface of the guide wheel at the top of the inner tank 8, the radius of the guide wheel can be approximated. R Equivalent to the thickness of the weir crest d .when R >0.67 h When the guide wheel is approximately equal to a broad-crested weir, the pump flow rate can be calculated using formula (17). R ≤ 0.67 h At that time, the guide wheel is approximately a rectangular sharp-edge weir, and the weir flow coefficient is taken as... C w ≈ 1.84 .

[0055] In this embodiment, the equivalent overflow hole in the middle of the inner tank 8 is temporarily ignored, and the width of the wide-top weir is... B= 730 mm, the height difference between the centerline of the water pump outlet 1 and the centerline of the outlet 1. H = 947 mm, number of weirs N = 4, requiring weir head h = 10 mm, R = 14.5mm > 0.67 h Assuming the weir flow coefficient C w ≈ 1.7 According to equation (17), we can obtain Q 0≈ 297.8 L / min, v 0 ≈ 2.53 m / s.

[0056] Calculate the pipeline losses at each level in the pipeline system according to formula (24), and plot the location, specifications, resistance coefficient, and corresponding hydraulic losses of components such as straight pipes, tees, and 90° bends with uniform cross-sections in Table 3. The total pipeline losses in Table 3 are then plotted. H tl Substituting ≈ 3.2 m into equations (6) and (7), we can obtain the pump outlet pressure. p 0 ≈ 44088 Pa, pump head H bump ≥4.157m. Therefore, for water pump selection, the outlet performance parameters must meet the following requirements: flow rate. Q bump ≥ 297.8 L / min, head H bump ≥ 4.157m.

[0057] In this embodiment, the initial pump selection was: 18m head, 258 L / min flow rate, 1.5 kW power, and 50 Hz frequency. After being put into operation on-site, the pipeline system in this section experienced a significant temperature increase, so a frequency converter was installed to change the pump frequency to 38 Hz. According to the similarity law, the pump flow rate... Q Yangcheng H and power P e With rotational speed oh It approximately satisfies the following relationship (27) When the frequency conversion coefficient k When Hz = 38 Hz / 50 Hz = 0.76, the pump flow rate increment Q ≈ twenty four% Q Power increment Pe ≈ 56% P e On-site test results show that the system temperature rise problem was effectively improved after frequency conversion. (Based on the approximate flow rate of the water pump after frequency conversion...) Q ≈ 196 L / min is the initial condition. Substituting this into equation (16) yields the weir head. h ≈ 7.57 mm. The total pipeline losses in Table 4... H tl Substituting ≈ 1.391 m into equations (6) and (7), we can obtain the water pump outlet pressure. p 0 ≈ 24390 Pa, pump head H bump ≥2.345 m. The calculation results of the simplified model and the field test results ( h The thickness is approximately 7 mm, which objectively confirms the applicability of this model for this type of working condition. The relevant calculation process parameters are shown in Table 4.

[0058] Table 3 Physical parameters of the piping system ( h = 10 mm)

[0059] *1 The inner diameter of the water pump outlet F Based on 50 mm; *2 Re = vd / υ The density of deionized water at 55℃ is approximately 985.7 kg / m³. 3 kinematic viscosity u Approximately 0.516 mm 2 / s, 1e5 means 1 10^5; *3 N / A This indicates that the parameter was not applied.

[0060] Table 4 Physical parameters of the piping system ( h ≈ 7.57 mm

[0061] In summary, this invention combines classical computational fluid dynamics theory with empirical formulas for overflow weirs of different shapes. Under specified conditions of piping system, pump flow rate, and head, it establishes an engineering design model for controlling the weir head. This model can predict friction loss and local losses in the piping system, and determine the flow rate of the central circular overflow orifice and the top weir head and flow rate within the tank. Based on the obtained flow rates, the inlet valve opening is adjusted to control the inlet flow rate, maintaining a constant liquid level. This ensures stable liquid level and flow within the tank, enhancing the degreasing and cleaning effect on electronic devices. Simultaneously, given a specified piping system and weir head target, it can determine the necessary pump flow rate and head to achieve the desired target, reducing operating energy consumption, improving energy efficiency, optimizing equipment selection, reducing equipment size, ensuring smooth water replenishment, guaranteeing unobstructed pipeline drainage without additional impact, stabilizing the flow field and liquid level, thereby improving cleaning and degreasing effects.

[0062] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE, characterized in that, include: Step 1: Construct a calculation model for the water supply head of the cleaning tank by combining Bernoulli's equation with pipeline losses; Step 2: Constructing the flow calculation model for the overflow weir. The method for constructing the flow calculation model for the overflow weir includes: S1: Construct a calculation model for the flow rate of the top overflow weir; S2: Construct a weir flow calculation model for the central overflow orifice; S3: Construct a flow rate calculation model for a rectangular weir orifice; S4: Construct a flow calculation model at the water pump outlet; Step 3: Construct a calculation model for pipeline losses to obtain the flow head that satisfies the condition of the top weir. h The inlet boundary conditions at that time, and the minimum flow rate and head required by the water pump; Step 4: Based on the obtained minimum flow rate and head, adjust the opening of the inlet valve to control the inlet flow rate and keep the liquid level constant.

2. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 1, characterized in that, In step one, considering pipeline losses, a modified Bernoulli equation is constructed. The modified Bernoulli equation is as follows: （2） In the formula, p The average pressure of the fluid in any cross-section of the pipeline system, expressed in Pa; v Let be the average flow velocity of the fluid in any cross-section of the pipeline system, in m / s; ρ The density of the fluid in any cross-section of the pipeline system, kg / m³ 3 ; H Let be the average height difference, in meters, of the fluid relative to a reference surface in any cross-section of the piping system; where the subscripts 0 and 1 represent any two different cross-sections in the piping system, respectively. H tl Let m be the pipe loss for streamlined particles between two different cross sections; g The acceleration due to gravity is m / s². 2 ; p / ρg The pressure head of streamlined particles is expressed in meters (m). v 2 / 2g Let be the velocity head of the streamlined particle, in meters (m).

3. The method for constructing a process tank head control model for electroplating equipment based on ODE according to claim 2, characterized in that, The flow rate of the top overflow weir is calculated in two ways depending on its thickness; When the thickness of the dam crest δ >0.6 h At that time, the weir flow rate is calculated using an empirical formula: （8） When the thickness of the dam crest δ ≤0.6 h At that time, the weir flow rate was calculated using Francis' semi-empirical formula: （9） In the formula, δ Where is the thickness of the weir crest, in meters; and the weir flow coefficient is... C w ≈ 1.4 ~ 1.7, ; B The width of the broad-crested weir is in meters (m). Q top The flow rate at the top weir is m. 3 / s; h The head of the weir is measured in meters (m).

4. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 3, characterized in that, The formula for calculating the weir flow rate of the central overflow orifice is: （10） （11） In the formula, C v An empirical coefficient characterizing the effect of fluid viscosity on flow velocity, with a unit of 1; C c The contraction coefficient is expressed in units of 1; the orifice flow coefficient. C d = C v C c The unit is 1; A The overflow orifice area is m. 2 ; Q mid The flow rate at the central overflow orifice is m. 3 / s; v The average overflow velocity is expressed in m / s. H c Let be the height difference between the center of the hole and the free liquid surface, in meters (m).

5. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 4, characterized in that, The formula for calculating the flow rate of the rectangular weir orifice is: （12） For the incremental flow d Q r In the interval ( H u , H d Integrating within the inner quadrant yields: （13） Considering the effect of the contraction section, the above equation can be simplified to （14） When the liquid level is within the rectangular weir orifice, for d Q r In the interval (0, ... H d Integrating within the inner quadrant yields... （15） In the formula, C d The orifice flow coefficient, H d The height difference between the bottom of the orifice and the liquid surface, in meters (m). H u The height difference between the top of the orifice and the liquid surface, in meters (m). Q r The flow rate of the rectangular weir orifice is m. 3 / s; b The area increment d of the rectangle A Width, m; d h The area increment d of the rectangle A The height, in meters; h The area increment d of the rectangle A The height difference between the geometric center and the liquid surface, in meters (m); d A m is the area increment of the rectangle. 2 ;d Q r The area increment d of the rectangle A Incremental traffic within, m 3 / s.

6. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 5, characterized in that, The formula for calculating the flow rate at the water pump outlet is: （16） In the formula, N 1 represents the number of identical top overflow weirs in the system. N 2 represents the number of overflow holes in the middle section. N 3 represents the number of rectangular weir orifices in the system. Q 0 represents the water pump outlet flow rate, in m³ / s. 3 / s.

7. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 1, characterized in that, The formula for calculating pipeline losses is as follows: （18） In the formula, H tl For pipeline losses, m; M H represents the number of uniform straight pipes in the piping system. fl,i For the first i Friction loss along a uniform straight pipe, m; H ll,j For the first j The local loss of a local component, m.

8. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 7, characterized in that, The friction loss H fl The calculation formula is: （19） In the formula, λ The friction factor of a straight pipe. l Let be the length of the straight pipe, in meters (m). d Let be the inner diameter of the straight pipe, in meters (m). g The acceleration due to gravity is m / s². 2 ; v The velocity of the liquid is expressed in m / s. The local loss H ll The calculation formula is: （21） In the formula, v The average flow velocity across the cross section is given in m / s. ζ This is the local drag coefficient, with a unit of 1.

9. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 8, characterized in that, The head of the water pump H bump Should meet: （7） In the formula, H bump Let be the pump head, in meters (m).

10. The method for constructing a process tank and weir flow head control model for electroplating equipment based on ODE according to claim 3, characterized in that, The top weir flow head h The inlet boundary conditions are: （17） （26） In the formula, λ i For the first i The friction coefficient of a uniform straight pipe, in units of 1; l i For the first i The length of a uniform straight pipe, in meters; d i For the first i The inner diameter of a uniform straight pipe, in meters; v i For the first i The average flow velocity in a uniform straight pipe, m / s; v j For the first j Local resistance coefficient of individual components ζ i The average flow velocity of the corresponding cross section, in m / s.

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