A solder paste temperature mechanism modeling and soft-sensing method for ground working conditions

Abstract

This invention belongs to the field of laser soldering modeling technology, and relates to a method for modeling and soft-sensing the solder paste temperature mechanism under grounding conditions. The method includes: establishing a two-dimensional thermal conductivity differential equation for the ground plane during solder paste heating based on the law of conservation of energy and Fourier's law of heat conduction, analyzing the thermal conductivity characteristics of the ground plane, and determining boundary conditions; discretizing the two-dimensional thermal conductivity differential equation using the finite element method, and constructing a two-dimensional temperature field model of the ground plane based on the boundary conditions; combining an existing non-grounded laser soldering thermodynamic model with the two-dimensional temperature field model to obtain a grounded laser soldering thermodynamic model; collecting relevant parameters during the target laser soldering process under grounding conditions, inputting them into the grounded laser soldering thermodynamic model, and outputting the predicted solder paste temperature. This invention establishes a thermodynamic model of the relationship between solder paste temperature and power under grounding conditions, achieving accurate prediction of solder paste temperature under grounding conditions.

Description

Technical Field

[0001] This invention relates to the field of laser soldering modeling technology, and in particular to a method for modeling and soft measurement of solder paste temperature mechanism under grounding conditions. Background Technology

[0002] As modern electronic devices continue to evolve towards miniaturization, integration, and high performance, soldering technology plays an increasingly important role in electronic assembly. As an advanced soldering method, laser soldering, with its advantages of high efficiency, precision, and non-contact operation, has been widely used for interconnecting microelectronic devices. However, existing laser soldering technologies are mostly based on ungrounded models, neglecting the impact of grounding effects on the soldering process. In certain application scenarios, this deficiency can lead to unstable soldering quality and even equipment damage. Therefore, this invention proposes a modeling and soft measurement method for solder paste temperature mechanisms under grounded conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a modeling and soft measurement method for solder paste temperature mechanism under grounding conditions. Based on the existing ungrounded model, the temperature field of the ground plane during the solder paste heating process is analyzed to obtain the heat conducted to the ground plane. A thermodynamic model of the relationship between solder paste temperature and power under grounding conditions is established to achieve accurate prediction of solder paste temperature under grounding conditions.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for modeling and soft sensing of solder paste temperature mechanism in grounding conditions, comprising:

[0006] Based on the law of conservation of energy and Fourier's law of heat conduction, a two-dimensional thermal conductivity differential equation for the ground plane during the solder paste heating process is established, and the thermal conductivity characteristics of the ground plane are analyzed to determine the boundary conditions.

[0007] The two-dimensional thermal conductivity differential equation is discretized using the finite element method, and a two-dimensional temperature field model of the ground plane is constructed by combining the boundary conditions.

[0008] By combining the existing ungrounded laser soldering thermodynamic model with the two-dimensional temperature field model, a grounded laser soldering thermodynamic model is obtained.

[0009] Collect relevant parameters during the laser soldering process of the target under grounding conditions, input them into the grounded laser soldering thermodynamic model, and output the predicted solder paste temperature.

[0010] Optionally, the two-dimensional thermal conductivity differential equation is:

[0011]

[0012] Where ρ represents the ground plane density, c represents the ground plane specific heat capacity, T represents the ground plane temperature field, t represents the heating time, λ represents the ground plane thermal conductivity, and x and y represent the coordinates on the two-dimensional spatial coordinate axes, respectively.

[0013] Optionally, the ground plane density ρ, ground plane specific heat capacity c, and ground plane thermal conductivity λ in the two-dimensional thermal conductivity differential equation are obtained by setting up multiple sets of experiments and using an iterative control algorithm. The identification process includes:

[0014] S1. Arrange multiple thermocouple temperature measuring wires on the ground plane to collect temperature data of several measuring points on the ground plane during the solder paste heating process.

[0015] S2, Setting Parameters The initial value is determined, and the ground plane temperature field is calculated based on the initial value;

[0016] S3. Compare the calculated temperature field with the measured temperature data, and adjust the parameters according to the error results.

[0017] S4. Utilize the adjusted parameters The value is returned in S2 to calculate the ground plane temperature field. This process is repeated from S2 to S4 until the error between the calculated and measured temperatures is within a preset range. The parameters at this point are then... This is determined as the final parameter value.

[0018] Optionally, the boundary conditions are:

[0019]

[0020] Where T represents the ground temperature field and n represents the unit vector of the outward normal of the boundary surface.

[0021] Optionally, the two-dimensional heat conduction differential equation is discretized using the finite element method, and a two-dimensional temperature field model of the ground plane is constructed by combining the boundary conditions, including:

[0022] The ground plane is divided into triangular elements on the two-dimensional spatial coordinate axis using the finite element method, resulting in multiple triangular elements. Each triangular element and all its nodes and edges are then numbered.

[0023] The element stiffness matrix of each triangular element is calculated, the matrix of each triangular element is embedded into the corresponding position of the global matrix, and boundary conditions are introduced to finally form a two-dimensional temperature field model of the ground plane.

[0024] Optionally, the two-dimensional temperature field model is:

[0025] (T k )′=(A′) -1C′-(A′) -1 A"T ir ;

[0026] Among them, (T) k )′ indicates that it is related to T k The relevant matrix, T k Let A' and A'' represent the temperature field at time k on the ground plane, respectively. A' and A''' are matrices composed of several elements of the global stiffness matrix A, and C' represents the temperature field at time k on the ground plane. k-1 The relevant matrix, T k-1 T represents the temperature field at time k-1 on the ground. ir The temperature of the solder paste is measured by a thermocouple.

[0027] Optionally, the thermodynamic model for grounded laser soldering is:

[0028]

[0029] in, The temperature of the solder paste at time k+1 is represented by m. sp α sp c sp A sp h sp These represent the solder paste's mass, absorption rate, specific heat capacity, heat dissipation area, and heat dissipation coefficient, respectively. Let P(k) represent the solder paste temperature at time k, P(k) represent the laser power at time k, T0 represent the room temperature, c and m represent the specific heat capacity and mass of the ground plane, respectively, and a and b are two coefficient parameters obtained after the transformation of the two-dimensional temperature field model. Δt represents the average temperature of the ground plane at time k, P represents the laser power, and Δt represents the heating time interval.

[0030] The beneficial effects of this invention are as follows:

[0031] This invention proposes a mechanism modeling and soft measurement method for solder paste temperature under grounded conditions, based on existing temperature-power relationship models for ungrounded laser soldering paste. By establishing a mechanism-driven prediction model, indirect measurement of solder paste temperature is achieved. First, based on the law of conservation of energy and Fourier's law of heat conduction, a mathematical model of the grounding plate temperature field is established, and unknown parameters under grounded conditions are identified through multiple sets of experiments. Then, the heat absorbed by the grounding plate during the soldering process is calculated using the established temperature field model, and combined with the existing temperature-power relationship model for ungrounded conditions to construct a solder paste temperature prediction model suitable for grounded conditions. This model, based on easily measurable parameters such as input power, realizes the soft measurement function of solder paste temperature. By comparing the prediction results with measured data, the high accuracy and reliability of the proposed grounding thermodynamic model are verified. This method eliminates the need for direct measurement of solder paste temperature during the soldering process, providing effective support for temperature monitoring and control in laser soldering, and has significant engineering application value. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the 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.

[0033] Figure 1 This is a schematic diagram of the grounding plate according to an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the triangular coordinate radial transformation according to an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of the triangular division method for the grounding plate according to an embodiment of the present invention;

[0036] Figure 4 1.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin pad is 2×10. -5 A comparison chart of temperature measurement and readings under the condition of 14.135W constant power heating for 10.5s with a mass of solder paste (kg);

[0037] Figure 5 1.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin tray is 2×10. -5 A schematic diagram showing the temperature deviation under constant power heating of 14.135W for 10.5s with a mass of 1 kg of solder paste;

[0038] Figure 6 1.5 × 10⁻⁶ in this embodiment of the invention -3The radius of the tin tray is 2×10. -5 Comparison of temperature readings and measurements under constant power heating of 15.75W for 8 seconds with a mass of solder paste (kg);

[0039] Figure 7 1.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin tray is 2×10. -5 Schematic diagram of temperature deviation under constant power heating of 15.75W for 8 seconds with a mass of solder paste (kg);

[0040] Figure 8 For the 2×10 of the embodiments of the present invention -3 The radius of the tin tray is 4×10. -5 A comparison chart of temperature measurement and reading data under constant power heating of 19.635W for 11 seconds with a mass of solder paste (kg);

[0041] Figure 9 For the 2×10 of the embodiments of the present invention -3 The radius of the tin tray is 4×10. -5 Schematic diagram of temperature deviation under constant power heating of 19.635W for 11s with a mass of 1 kg of solder paste;

[0042] Figure 10 For the 2×10 of the embodiments of the present invention -3 The radius of the tin pad is 4.7 × 10⁻⁶. -5 A comparison chart of temperature measurement and reading data under constant power heating of 21.71W for 9 seconds with a mass of solder paste (kg);

[0043] Figure 11 For the 2×10 of the embodiments of the present invention -3 The radius of the tin pad is 4.7 × 10⁻⁶. -5 Schematic diagram of temperature deviation under constant power heating for 9 seconds with a mass of 21.71W of solder paste;

[0044] Figure 12 2.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin pad is 6.3 × 10 m. -5 A comparison chart of temperature measurement and readings under constant power heating of 25.683W for 8.5s with a mass of solder paste (kg);

[0045] Figure 13 2.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin pad is 6.3 × 10 m. -5 A schematic diagram showing the temperature deviation under constant power heating of 25.683W for 8.5 seconds with a mass of solder paste (kg);

[0046] Figure 14 2.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin pad is 6.3 × 10 m. -5A comparison chart of temperature measurement and reading data under constant power heating of 27.093W for 7.5s with a mass of 27.093kg of solder paste;

[0047] Figure 15 2.5 × 10⁻⁶ in this embodiment of the invention -3 The radius of the tin pad is 6.3 × 10 m. -5 A schematic diagram showing the temperature deviation under constant power heating for 7.5 seconds with a solder paste mass of 27.093W;

[0048] Figure 16 This is a flowchart of a solder paste temperature mechanism modeling and soft measurement method for grounding conditions according to an embodiment of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] This embodiment proposes a method for modeling the temperature mechanism of solder paste under grounding conditions and for soft measurement, such as... Figure 16 As shown, it includes:

[0052] Based on the law of conservation of energy and Fourier's law of heat conduction, a two-dimensional thermal conductivity differential equation for the ground plane during the solder paste heating process is established, and the thermal conductivity characteristics of the ground plane are analyzed to determine the boundary conditions.

[0053] The two-dimensional thermal conductivity differential equation is discretized using the finite element method, and a two-dimensional temperature field model of the ground plane is constructed by combining the boundary conditions.

[0054] By combining the existing ungrounded laser soldering thermodynamic model with the two-dimensional temperature field model, a grounded laser soldering thermodynamic model is obtained.

[0055] Collect relevant parameters during the laser soldering process of the target under grounding conditions, input them into the grounded laser soldering thermodynamic model, and output the predicted solder paste temperature.

[0056] Specifically, this embodiment first establishes a two-dimensional thermal conductivity differential equation for the ground plane during the solder paste heating process based on the law of conservation of energy and Fourier's law, and analyzes it in conjunction with boundary conditions; then, the equation is discretized using the finite element method to obtain a two-dimensional temperature field model of the ground plane, and combined with the existing ungrounded laser soldering thermodynamic model to obtain the final grounded laser soldering thermodynamic model.

[0057] The existing thermodynamic model for ungrounded laser soldering is as follows:

[0058]

[0059] Where, ρ sp c sp V sp α sp A sp h sp T sp The parameters represent the density, specific heat capacity, volume, absorptivity, heat dissipation area, heat dissipation coefficient, and temperature of the solder paste, respectively; t represents the heating time; P represents the laser power; and T0 represents the room temperature. The term Pα represents the energy change of solder paste per unit time. sp This represents the energy absorbed by the solder paste per unit time, item A. sp h sp (T sp -T0) represents the energy dissipated from the solder paste into the air per unit time. Divide both sides of the equation by c. sp ,get:

[0060]

[0061] Based on experimental results, the heating process can be divided into three stages: T sp ≤160℃ (unmelted), 160℃≤T sp <180℃ (semi-melting), T sp ≥180℃ (complete melting), and in the ungrounded model described by equation (2), the parameters were tested using experimental data. and Perform segmentation identification.

[0062] It is worth noting that existing thermodynamic models for ungrounded laser soldering only consider grounded pads of uniform size and are based on assumptions using the lumped parameter method. In this embodiment, the solder paste is approximated as a spherical cap structure. Unlike the ideal assumptions in the lumped parameter method, heat conduction still occurs within the solder paste in reality. During heat dissipation, larger solder pastes have longer heat conduction paths, making internal heat transfer and dissipation more difficult. Therefore, the parameters obtained during heat dissipation identification are... It decreases as the solder paste size increases. Further analysis shows that the decreasing trend of this parameter is directly related to the solder paste half-pad size (r). Experimental verification revealed that the parameter combination... It exhibits good consistency under different size conditions. Therefore, this parameter and parameter can be compared based on experimental data. The identification was performed, and the results are shown in Table 1.

[0063] Table 1

[0064]

[0065] The change in energy per unit time of the solder paste during the heating process on the ground plane. Energy absorption term Pα sp and air heat dissipation item A sp h sp (T sp -T0) is the same as the ungrounded case, the difference being that the grounded condition adds a heat transfer process from the solder paste to the ground plane. A schematic diagram of the ground plane is shown below. Figure 1 As shown, it contains several pads of different sizes. Since the solder paste heating time is short, and the experimentally measured ground plane temperature field indicates that its influence from the solder paste heating is limited (experiments show that there is basically no temperature change at a distance of 0.01m from the center of the heated pads), and the copper oxide covering the ground plane surface reduces the air heat dissipation effect, for the sake of simplifying the calculation, it can be assumed that the ground plane does not dissipate heat to the air. Therefore, under grounding conditions, the energy transferred by the solder paste to the ground plane per unit time can be expressed as the energy change of the ground plane per unit time, i.e. Therefore, the grounding model can be initially represented as:

[0066]

[0067] Among them, c, m, T g Let represent the specific heat capacity, mass, and average temperature of the solder paste, respectively. Divide both sides of the above equation by the specific heat capacity c of the solder paste. sp After discretization, we can obtain:

[0068]

[0069] in, and Let represent the solder paste temperature at time k and the average temperature of the ground plane, respectively. Next, the average temperature will be calculated using the temperature field of the ground plane.

[0070] Based on the law of conservation of energy and Fourier's law, a differential equation for heat conduction of the ground plane is introduced. Considering that the ground plane is relatively thin overall, its thickness in the z-direction is negligible compared to the x and y directions; therefore, this paper establishes a two-dimensional heat conduction model only in the xy-plane. The two-dimensional heat conduction equation is as follows:

[0071]

[0072] Where ρ represents the grounding density, c represents the grounding specific heat capacity, T represents the grounding temperature field, t represents the heating time, λ represents the grounding thermal conductivity, and x and y represent the coordinates on the two-dimensional spatial coordinate axes. Dividing both sides of equation (5) by λ, we get:

[0073]

[0074] Since the area experiencing drastic temperature changes during heating is relatively small, and the edge of the grounding plate is covered, its boundary can be considered an adiabatic boundary, meaning no heat flow passes through it, which can be represented as:

[0075]

[0076] Where n represents the unit vector of the outward normal of the boundary surface.

[0077] The initial temperature distribution conditions are:

[0078] T 1 =T0 (8);

[0079] Among them, T 1 T0 represents the two-dimensional temperature field at the ground plane at time 1, where T0 represents room temperature.

[0080] Define the test function as v(x,y), and let the ground plane region be Ω. Then equation (7) can be written in the following weak form:

[0081]

[0082] By the rule of differentiation of multiplication, we can obtain:

[0083]

[0084] Therefore:

[0085]

[0086] Substituting equation (11) into equation (9), we get:

[0087]

[0088] From the divergence theorem and equation (7), we can obtain:

[0089]

[0090] Substituting equation (13) into equation (12), we get:

[0091]

[0092] Consider the following basis functions:

[0093]

[0094] set up Let represent the temperature of node i on the ground at time k, and let the coordinates of node i be (x, k). i y i Then we have:

[0095]

[0096] The summation symbol represents assembly summation in the finite element method, which means that matrix assembly is completed by embedding the stiffness matrices of each local element into the corresponding positions of the global stiffness matrix, rather than directly adding the values.

[0097] Let m be the number of nodes contained in the region Ω after spatial discretization, and define the test function as:

[0098]

[0099] Therefore, at time k, we have:

[0100]

[0101] Substituting equation (18) into equation (15), we obtain the following form:

[0102] AT k =BT k-1 (19);

[0103] Where A and B are m*m matrices, T k-1 With T k It is an m*1 vector, specifically as follows:

[0104]

[0105] In the finite element analysis of the temperature field of the mating ground, this embodiment uses triangular elements for discretization. To facilitate the construction of basis functions and numerical calculations, a coordinate eccentric transformation is applied to each triangular element to map the element from the physical coordinate system to the reference element (see [reference]). Figure 2 (See the schematic diagram of the triangular coordinate radial transformation shown). Local linear basis functions can be defined on the reference element. The interpolation condition is met: the value is 1 at the corresponding node and 0 at other nodes. Using this coordinate transformation, the basis functions and their gradients can be mapped back from the reference element to the physical element. This allows for the calculation of shape functions, element stiffness matrices, and load vectors on each element. Through the assembly process, each local matrix is ​​embedded into the global matrix, completing the finite element discretization and solution of the entire ground plane temperature field. The specific process is as follows:

[0106] When taking first-order linear basis functions, the expression of the basis functions on any unit can be defined as:

[0107]

[0108] Let the coordinates of the three nodes of the reference element be (0, 0), (1, 0), and (0, 1), and their corresponding basis functions be respectively. Then for have Therefore, we can conclude that: Therefore, in this unit:

[0109]

[0110] Similarly, in this unit:

[0111]

[0112] Consider an arbitrary triangular finite element with three node coordinates (x1, y1), (x2, y2), and (x3, y3). Through a coordinate affine transformation, the basis functions on the reference element can be mapped to this physical element, resulting in:

[0113]

[0114] When calculating the element stiffness matrix, the chain rule can be used to obtain:

[0115]

[0116] Then we have:

[0117]

[0118] Therefore, by the substitution formula for double integrals, we can obtain:

[0119]

[0120] From equation (24), we can see that, From equations (20) and (21), it can be seen that,

[0121] Similarly, we have:

[0122]

[0123] Substituting equations (27) and (28) into equation (19), the only unknown remains T. k Let BT k-1 =C, then equation (19) can be transformed into:

[0124] AT k=C (29);

[0125] Expanded to:

[0126]

[0127] In practice, the solder paste is evenly applied to the surface of the pads, and the pad surface is smooth, free of oxidation or impurities, ensuring an uninterrupted heat transfer path between the two, allowing heat to flow smoothly from the pads to the solder paste. Therefore, in this embodiment, to simplify the model and improve computational efficiency, it is assumed that there is good contact between the solder paste and the pads, and that the interface continuity condition is met, i.e., the solder paste temperature is the same as the pad temperature. The solder paste pads are introduced at points l1 to l2 on the ground plane. n The temperature condition, specifically the temperature at the heated pad. Point l i The temperature at that location is expressed as Let T ir The solder paste temperature T measured by a thermocouple sp Therefore, this can be set as a first-type boundary condition, expressed as:

[0128]

[0129] Introducing the first type of boundary condition represented by equation (31) into the ground plane temperature field model, taking position l1 as an example, it can be seen from equation (30) that for any i (i∈[1,m]), we have

[0130]

[0131] Then we can obtain equation (33) after introducing the first type of boundary conditions:

[0132]

[0133] From l1 to l n After processing all points in the above manner, the resulting equation can be written in the following form:

[0134] A′(T k )′=C′-A″T ir (34);

[0135] Finally, a two-dimensional temperature field model of the ground plane can be obtained:

[0136] (T k )′=(A′) -1 (C′-A″T ir )=(A′) -1 C′-(A′) -1 A″T ir (35);

[0137] During the ground plane heating process, thermocouples are placed at several pad locations around the heating pads, and the temperature during the heating process is recorded and denoted as T. f1 ~T fn Subsequently, an iterative control algorithm was used to adjust the model parameters. Perform overall identification. Specifically, first set the parameters. Initial values ​​were obtained, and the temperature field was calculated based on the ground plane model shown in equation (35); the calculation results were compared with the measured temperature T at each measuring point. f1 ~T fn By comparing each one, the corresponding error e is obtained. f1 ~e fn To mitigate the impact of local maximum errors and improve overall identification accuracy, the squares of each error are summed after retaining their signs to form a comprehensive error index e. f Based on this, the model parameters are adjusted according to the iterative formula. Progressive updates and optimizations are performed. During the iteration process, a maximum permissible error threshold and a maximum number of iterations are set. When the comprehensive error e... f The iteration terminates when the value is less than the threshold or the maximum number of iterations is reached, and the parameters obtained at this point are recorded. This serves as the identification result. Finally, the parameters obtained are calculated under multiple sets of experimental conditions. The results are averaged to obtain the final parameters. estimate.

[0138] As shown in equation (35), this two-dimensional temperature field is directly related to the solder paste temperature measured by the thermocouple. The average temperature T of the ground plane... g The temperature field of the ground plane can be calculated at each moment, as follows: When calculating the temperature field of the ground plane using the finite element method, a triangular partitioning method is adopted, where each triangular element represents a calculation unit, such as... Figure 3 As shown. The average temperature of the three nodes of each element is calculated as the temperature of that element, and the temperatures of all elements are averaged to obtain the average temperature T of the ground plane. g However, there is a problem here: calculating the solder paste temperature at time k requires knowing the average temperature of the ground plane at time k, which means knowing the temperature field of the ground plane. Solving for the temperature field of the ground plane at time k depends on the solder paste temperature at time k. Therefore, the temperature of each point in the ground plane temperature field needs to be expressed in terms of solder paste temperature. This has been achieved through equation (35), so the average temperature T of the ground plane is... g It can be represented as:

[0139] T g =a+bT sp (36);

[0140] Substituting equation (36) into equation (4) and rearranging, we get:

[0141]

[0142] Where, m sp This indicates the quality of the solder paste. Then, by substituting the grounding test data into equation (37) for calculation, the parameters can be obtained. The identification results are shown in Table 2:

[0143] Table 2

[0144]

[0145] To verify the accuracy of the established thermodynamic model (37), a comparative experiment was designed and conducted, and the model was simulated using Matlab. The specific scheme is as follows: Radius of 1.5 × 10⁻⁶ was selected. -3 m, 2×10 -3 m, 2.5×10 -3 Using the solder pads of size m as the experimental object, tests were conducted under different solder paste quality conditions. Simultaneously, a constant power mode was adopted, setting the laser emitter power to several different values, each corresponding to a different heating time. Subsequently, the above experimental parameters were substituted into the established model to obtain simulation results, which were then compared with actual experimental data. Specific comparison results are shown in Table 3. Figures 4-15 As shown, the results indicate that the simulation curves are highly consistent with the experimental data, thus verifying the effectiveness and accuracy of the model.

[0146] Table 3

[0147]

[0148] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for modeling and soft-sensing the temperature mechanism of solder paste under grounding conditions, characterized in that, include: Based on the law of conservation of energy and Fourier's law of heat conduction, a two-dimensional thermal conductivity differential equation for the ground plane during the solder paste heating process is established, and the thermal conductivity characteristics of the ground plane are analyzed to determine the boundary conditions. The two-dimensional heat conduction differential equation is discretized using the finite element method, and a two-dimensional temperature field model of the ground plane is constructed based on the boundary conditions. The two-dimensional temperature field model is as follows: ； in, This represents the matrix associated with Tk, where Tk represents the temperature field at time k on the ground plane. and Let A be a matrix composed of several elements of the global stiffness matrix A. This represents the matrix associated with Tk-1, where Tk-1 represents the temperature field at time k-1 on the ground plane. The temperature of the solder paste as measured by a thermocouple; The ground plane is divided into triangular elements on the two-dimensional spatial coordinate axis using the finite element method, resulting in multiple triangular elements. Each triangular element and all its nodes and edges are then numbered. Calculate the element stiffness matrix of each triangular element, embed the matrix of each triangular element into the corresponding position of the global matrix, and introduce boundary conditions to finally form a two-dimensional temperature field model of the ground plane. By combining the existing ungrounded laser soldering thermodynamic model with the two-dimensional temperature field model, a grounded laser soldering thermodynamic model is obtained. The grounded laser soldering thermodynamic model is as follows: ； in, This represents the solder paste temperature at time k+1. , , , , These represent the solder paste's mass, absorption rate, specific heat capacity, heat dissipation area, and heat dissipation coefficient, respectively. This represents the solder paste temperature at time k. This represents the laser power at time k. T 0 represents room temperature. c , m These represent the specific heat capacity and mass of the grounding plate, respectively. a , b These are the two coefficient parameters obtained after transforming the two-dimensional temperature field model. This represents the average temperature of the ground at time k. P Indicates laser power. Indicates the heating time interval; Collect relevant parameters during the laser soldering process of the target under grounding conditions, input them into the grounded laser soldering thermodynamic model, and output the predicted solder paste temperature.

2. The solder paste temperature mechanism modeling and soft measurement method for grounding conditions according to claim 1, characterized in that, The two-dimensional thermal conductivity differential equation is: ； in, ρ Indicates the density of the grounding plate. c Indicates the specific heat capacity of the grounding plate. T This indicates the temperature field of the ground plane. t Indicates heating time. λ Indicates the thermal conductivity of the ground plane. x , y These represent the coordinates on the two-dimensional coordinate axes, respectively.

3. The method for modeling and soft-sensing the temperature mechanism of solder paste for grounding conditions according to claim 1, characterized in that, The ground plane density in the two-dimensional thermal conductivity differential equation ρ Specific heat capacity of the ground c Thermal conductivity of the grounding plate λ The identification was achieved by setting up multiple sets of experiments and using an iterative control algorithm. The identification process included: S1. Arrange multiple thermocouple temperature measuring wires on the ground plane to collect temperature data of several measuring points on the ground plane during the solder paste heating process. S2, Setting Parameters The initial value is determined, and the ground plane temperature field is calculated based on the initial value; S3. Compare the calculated temperature field with the measured temperature data, and adjust the parameters according to the error results. ; S4. Utilize the adjusted parameters The value is returned in S2 to calculate the ground plane temperature field. This process is repeated from S2 to S4 until the error between the calculated and measured temperatures is within a preset range. The parameters at this point are then... This is determined as the final parameter value.

4. The method for modeling and soft-sensing the temperature mechanism of solder paste for grounding conditions according to claim 1, characterized in that, The boundary conditions are as follows: ； in, T This indicates the temperature field of the ground plane. n This represents the unit vector of the outward normal to the boundary surface.

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