A Modeling Method for Laser Soldering and a Feedforward-PI Control Method for the Model

Abstract

The present invention relates to the field of laser soldering modeling, and discloses a laser soldering modeling and a feedforward-PI control method for the model. The temperature field in the solder paste is established according to the law of conservation of energy and Fourier's law, and then a mathematical model for laser heating is established based on the lumped parameter method. According to this model, multiple groups of experiments are carried out to identify the complex parameters that are difficult to determine in the model, and the optimal model is obtained. Through the comparison of simulation experiment and actual experiment data, the accuracy of the laser soldering thermodynamic model established in this paper is proved. Finally, a feedforward-PI control method is designed based on the model. For other laser welding models, this model has a smaller temperature error, making the model results closer to the actual results. By comparing the traditional PID with the feedforward-PI control method, the temperature accuracy is improved, and the sum of the absolute values of the control quantity deviation is also smaller than that of the traditional PID control method, that is, energy is saved. The comparison results confirm that the feedforward-PI control effect is better, and the control performance has been significantly improved.

Description

Technical Field

[0001] The present invention relates to the field of laser soldering modeling, and specifically to a laser soldering modeling and a feedforward-PI control method for the model. Background Art

[0002] Laser soldering utilizes the high energy density of a laser to achieve rapid heating of a local or micro area to complete the soldering process. The key lies in the reasonable control of laser power distribution. It is mainly used for the connection of electronic components on printed circuit boards. The integrated circuit leads are heated by laser radiation, and heat is transferred to the substrate through a soldering flux or pre-placed solder. When the temperature reaches the soldering temperature, the soldering flux and solder melt, and the substrate and the leads are wetted to form a connection, which can well enable electronic products to gradually develop towards the direction of miniaturization of volume, complexity of structure, and integration of functions, and at the same time improve their reliability while reducing the difficulty of processing and soldering. Since the laser power and the properties of the solder paste have a greater impact on the temperature accuracy, there has been less modeling of the laser soldering system in the past, and the established mathematical model has a large gap with the actual production application. Therefore, establishing an accurate model is an important task in the field of laser soldering at present. In this paper, a thermodynamic model under laser heating is established for the welding process, and a thermodynamic mathematical model between parameters such as laser power, spot area, heating time, and solder paste quality and the temperature of solder spreading and solder joint forming is given, and a feedforward control method is performed based on the model.

[0003] The laser welding process is a complex production process, and the establishment of a mathematical model is also one of the more difficult tasks because there are many factors causing modeling errors, and the parameters among them are difficult to determine. For example, the absorption rate of the solder paste to the laser and the heat dissipation coefficient of the solder paste are all functions related to temperature. The present invention identifies the relevant parameters difficult to determine in the laser soldering model through multiple groups of experiments, thereby improving the accuracy of the model. Based on this newly established thermodynamic model, feedforward control is performed, which can effectively improve the temperature accuracy of the system and reduce energy loss. For this reason, we propose a laser soldering modeling and a feedforward-PI control method for the model. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] In view of the deficiencies of the prior art, the present invention provides a laser soldering modeling and a feedforward-PI control method for the model, which improves the accuracy of establishment in the field of laser soldering, and provides a feedforward-PI control method for the laser soldering model, which improves the temperature control accuracy of laser soldering.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the present invention provides the following technical solution: A laser soldering modeling and a feedforward-PI control method for the model, comprising the following steps:

[0008] Step 1: Establish the most basic mathematical relationship that the temperature field of the solder paste should satisfy according to the law of conservation of energy and Fourier's law;

[0009] Step 2: Based on the lumped parameter method, convert the heat exchanged at the boundary into a volume source term of the entire surface, add the total surface heat dissipation to the basic mathematical relationship, and establish a thermodynamic mathematical model under laser heating during the welding process;

[0010] Step 3: Design multiple groups of experiments for the model, identify the complex parameters in the model, and obtain the optimal model of laser soldering;

[0011] Step 4: Perform a feedforward-PI control method based on the optimal model of laser soldering.

[0012] Preferably, the most basic mathematical relationship in the first step is:

[0013]

[0014] where a is the thermal diffusivity, defined as which is the Laplace operator of temperature, is the generalized heat source, ρ is the solder paste density, and c is the specific heat capacity of the solder paste.

[0015] Preferably, the thermodynamic model in the second step is:

[0016]

[0017] where ρ is the solder paste density, c is the specific heat capacity of the solder paste, P is the laser power, α is the absorption rate, A is the surface area of the solder paste, h is the surface heat transfer coefficient, T is the temperature, t is the time, and T0 is the ambient temperature.

[0018] Preferably, the h, c, and α are obtained by identifying multiple groups of experiments. The process is as follows: Since the heat transfer coefficient h and the specific heat capacity c are determined by the properties of the material itself and are independent of whether it is heated, substitute the experimental data into the model in the heat dissipation stage to obtain the relevant parameter h / c;

[0019] Since the state of the solder paste will affect the surface roughness of the solder paste and thus affect the absorption rate, substitute the obtained h / c and the experimental data in the heating stage to find α / h.

[0020] Preferably, the state of the solder paste will affect the surface roughness of the solder paste and thus affect the absorption rate. The heating process of the solder paste is divided into three stages: preheating, melting, and continuous heating after melting. Therefore, the value of α / h needs to be calculated in stages.

[0021] Preferably, the optimal model of laser soldering in the third step is as follows:

[0022]

[0023] where T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, P is the power, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period, and T0 is the ambient temperature.

[0024] Preferably, the optimal model of laser soldering in the fourth step is used for feedforward control. According to the optimal model T(k) and the target function T tar (t), the output u f (k) of the feedforward controller is obtained. Then, according to the deviation value e(k) between the output temperature and the target, the output power u p (k) of the PI controller is calculated. The sum of u p (k) and u f (k + 1) is taken as u(k + 1) as the input;

[0025] where

[0026]

[0027]

[0028] T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, P is the power, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period, T0 is the ambient temperature. In the formula, u p (k) is the output power (W) of the PI controller at the k-th moment, u f (k) is the output power (W) of the feedforward controller at the k-th moment, e(k) is the temperature error (°C) at the k-th moment during heating, K P and K I are the proportional coefficient and the integral coefficient respectively.

[0029] (III) Beneficial Effects

[0030] Compared with the prior art, the present invention provides a method for laser soldering modeling and feedforward-PI control of the model, having the following beneficial effects:

[0031] 1. The laser soldering modeling and the feedforward-PI control method of the model. For the laser soldering modeling method, there are few such methods and the temperature accuracy is low. The present invention significantly reduces the temperature error. It is still applicable to the cases of different powers, different solder paste qualities, and different pad areas. It is not only simple to implement in practice and has better effects, but is very suitable for wide use in the laser soldering modeling process, and is also conducive to providing a more effective model for other control methods of laser soldering in the future. Based on the feedforward-PI control algorithm, the present invention enables the laser soldering system to obtain better control performance.

[0032] 2. The laser soldering modeling and the feedforward control method of the model have good industrial performance and can adapt to the cases of different power ranges and different solder paste composition ratios in different laser welding equipment. The modeling method of the present invention can be applied to the modeling process of various types of laser equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is an energy balance analysis diagram of a microelement parallelepiped randomly taken from the solder paste;

[0034] Figure 2 It is a laser welding workstation with an infrared temperature measurement system;

[0035] Figure 3 It is a laser heating curve graph under different powers;

[0036] Figure 4 For the pad radius of 2×10 -3 m and the laser power of 8.2 W, it is a comparison diagram of the experimental curve and the simulation curve;

[0037] Figure 5 It is a flow chart of the feedforward PID control method;

[0038] Figure 6 It is a simulation diagram of the traditional PID control, the target curve, and the output power diagram;

[0039] Figure 7 It is a simulation diagram of the feedforward-PI control, the target curve, and the output power diagram;

[0040] Figure 8 It is a simulation diagram of the optimal feedforward-PI control, the target curve, and the output power diagram. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0042] Please refer to Figure 1-8 , a laser soldering modeling and feedforward-PI control method for the model, including the following content:

[0043] The laser soldering equipment of the present invention mainly consists of a laser emitter, a temperature measurement system, a motor control system, etc. The motor controller is used to control the moving stage to move the solder joint directly below the laser emitter, adjust the defocus amount, and turn on the laser so that a semiconductor laser beam is focused on the solder joint through an optical fiber and a focusing lens. The temperature of the solder joint is measured with an infrared thermometer to ensure that the solder paste reaches the target temperature. After the solder paste melts, the welding process is completed. The moving stage places the sample board under the infrared thermometer to detect each position on the surface of the solder pad. The data acquisition, platform positioning, and vision system are all controlled by a computer, providing a complete system. The vision system is controlled by a computer, providing a fully automatic detection process.

[0044] The modeling method of the present invention derives the most basic mathematical relationship according to Fourier's law and the law of conservation of energy, that is, the heat flux of the introduced microelement body on the three microelement surfaces of the solder paste x = x, y = y, z = z, and the heat flux of the derived microelement body on the three surfaces of x = x + dx, y = y + dy, z = z + dz. Then, the thermodynamic model of laser soldering is derived by the lumped parameter method, and finally, experiments are designed to identify the relevant parameters in the model to obtain the optimal model. The derivation process of the model is detailed as follows:

[0045] Analyze the energy balance in an arbitrary parallelepiped microelement in the solder paste. Let the internal energy value in the solder paste be It represents the heat energy generated or consumed per unit volume of the solder paste per unit time (positive for generation and negative for consumption), and the unit is W / m 3 . Assume that the thermophysical properties of the solder paste are functions of temperature.

[0046] Similar to the fact that the heat flux density vector at any point in space can be decomposed into components in three coordinate directions, the heat flux in any direction can also be decomposed into component heat fluxes in the x, y, and z coordinate axes directions, as shown in Figure 1 where φ x , φ y , and φ z are shown. The heat flux introduced into the microelement body through the three microelement surfaces of x = x, y = y, z = z can be written according to Fourier's law as:

[0047]

[0048] where (φ x ) x represents the component of the heat flux in the x - direction, φ x , at the value of x, and so on. λ is the thermal conductivity. The heat flux through the three surfaces x = x + dx, y = y + dy, and z = z + dz for the infinitesimal element can also be written according to Fourier's law as follows:

[0049]

[0050] For the infinitesimal element, according to the law of conservation of energy, there is the following heat balance relationship within any time interval:

[0051] Total heat flux into the infinitesimal element + Heat generated by internal heat sources within the infinitesimal element =

[0052] Total heat flux out of the infinitesimal element + Increment of the thermodynamic energy (i.e., internal energy) of the infinitesimal element (3)

[0053] The expressions for the other two terms in Equation (3) are:

[0054]

[0055] where ρ, c, and t are the density, specific heat capacity, heat generated by internal heat sources per unit volume per unit time, and time of the infinitesimal element respectively.

[0056] Substituting Equations (1), (2), and (4) into Equation (3) and after rearrangement, we get:

[0057]

[0058] where ρ, c, λ, and the source term can all be variables.

[0059] When laser heating solder paste, when the thermal resistance of heat conduction inside the solder paste is much smaller than the heat transfer resistance on its surface, the temperature inside the solder paste tends to be uniform at any moment, so that it can be considered that the entire welding material is at the same temperature at the same instant. At this time, the temperature to be solved is only a univariate function of time t and is independent of the spatial coordinates. It is considered that the originally continuously distributed mass and heat capacity of the material are aggregated to one point, and there is only one temperature value. Based on this simplified analysis that ignores the internal thermal resistance of the object - the lumped parameter method, a thermodynamic model for the laser heating process is established.

[0060] There is a solder paste with an arbitrary shape, whose volume is V, surface area is A, and has a uniform initial temperature T0. At the initial moment, it is suddenly placed in a constant - temperature environment of T∞ In the fluid, let T ∞ > T0, the surface heat transfer coefficient h between the solder paste and the fluid and the physical property parameters of the solder paste remain constant, that is:

[0061]

[0062] where a is the thermal diffusivity, defined as which is the Laplace operator of temperature, is the generalized heat source, ρ is the solder paste density, and c is the specific heat capacity of the solder paste. Ignoring the internal thermal resistance of the object, the temperature is independent of the spatial coordinates, so the second-order derivative term of the temperature in the formula is zero. Then the above formula is simplified to:

[0063]

[0064] Therefore, after the laser heating is completed, the heat transferred per unit time and per unit volume is:

[0065]

[0066] Similarly, during the laser heating process, the heat transferred per unit time and per unit volume is:

[0067]

[0068] where P is the laser power, α is the absorption rate, A is the surface area of the solder paste, and h is the surface heat transfer coefficient. Substituting Equation (8) and Equation (9) into Equation (7) respectively, the thermodynamic models for the heat dissipation stage and the laser heating stage can be obtained:

[0069]

[0070] Since the absorption rate, specific heat capacity, and surface heat transfer coefficient of the solder paste will change with the temperature of the solder paste, the measurement of these parameters is very demanding. Therefore, experiments are designed for these parameters. First, use a power meter, precision mass meter, etc. to measure the relevant parameters as shown in the following table, and then identify the unknown parameters of the model through the experimental data.

[0071] Table 1: Relevant Parameters

[0072]

[0073]

[0074] Substitute the experimental data in the heat dissipation stage into Equation (10) to obtain the relevant parameter h / c in the model. Since the heat dissipation coefficient h and the specific heat capacity c are determined by the properties of the material itself and are independent of whether it is heated or not. Since the laser welding process is divided into 4 stages, namely preheating, activation, heat preservation and cooling. During the laser welding process, the state of the solder paste will affect the surface roughness of the surface solder paste and thus affect the absorption rate. Therefore, substitute the obtained h / c and the experimental data in the heating stage into Equation (10) to obtain α / h in the first three stages respectively. See the following table.

[0075] Table 2: Relationship table of model identification parameters h / c, α / h varying with temperature (T)

[0076]

[0077] The data obtained from the above identification are only the actual results in this example, and this result is only applicable to this example.

[0078] Transform Equation (10) to get:

[0079]

[0080] where T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, P is the power, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period, and T0 is the ambient temperature.

[0081] To verify the accuracy of the newly established thermodynamic model, design an experiment and use Matlab to simulate the model (Equation (11)). Experimental scheme: Conduct experiments using pads with a radius of 2×10 -3 m, the mass of the solder paste is 3.75×10 -5 g, adopt the constant power mode to set the power of the laser emitter to 8.2W to carry out the laser brazing process, set the heating time to 13s respectively, substitute all parameters into the model, and then compare the experimental data with the simulation. The results confirm that the simulation and the experiment have good consistency, indicating the accuracy of the model. Based on this model, control methods can be adopted to improve the temperature accuracy during laser welding.

[0082] Based on the optimal model Equation (11), adopt the feedforward-PI control method, and calculate the corresponding power u tar (k) according to the model T(k) and the target temperature function T f (t).

[0083]

[0084]

[0085] where the unit period of t is 0.01 s, T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, and u f (k) is the output power (W) of the feedforward controller at the k-th moment, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period (0.01 s), and T0 is the ambient temperature.

[0086] Calculate the output power compensation u p (k) of the PI controller at the next moment according to the temperature deviation.

[0087]

[0088] where e(k) is the temperature error at the k-th moment during heating, i.e., T(k) - T tar (k) (°C), and K P and K I are the proportional coefficient and the integral coefficient respectively.

[0089] Verify the feedforward-PI control method and simulate the model using Matlab. Compare the traditional PID with the feedforward-PI control method as shown in the following table. The temperature accuracy has been improved, and the absolute value of the control variable deviation is also smaller, which indicates that the feedforward control method saves energy. The comparison results confirm that the feedforward-PI control effect is better, and the control performance has been significantly improved.

[0090] Table 3: Comparison between the positional PID control and the feedforward-PI control

[0091] Comparison Variance Degree of power oscillation Kp Ki Traditional PID control 0.045 1.95 20 1 Feedforward-PI control 0.015 1.95 20 1 Feedforward-PI control 0.2 0.2 1 0.1

[0092] The modeling method of the laser soldering process based on the lumped parameter method and the feedforward-PI control algorithm based on the model of the present invention are simple to implement and can make good use of experimental data. The experimental data are extremely important resources required for the identification parameters in the model, and the model is very suitable for use in the laser soldering modeling process. The control method improves the temperature accuracy and is suitable for controlling the soldering temperature during the laser welding process.

[0093] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A laser soldering modeling and feedforward-PI control method for the model, characterized in that It includes the following steps: The first step: Establish the most basic mathematical relationship that the temperature field of the solder paste should satisfy according to the law of conservation of energy and Fourier's law; The second step: Based on the lumped parameter method, convert the heat exchanged at the boundary into a volume source term of the entire surface, add the total surface heat dissipation to the basic mathematical relationship, and establish a thermodynamic mathematical model under laser heating during the soldering process; The third step: Design multiple groups of experiments for the model, identify the complex parameters in the model, and obtain the optimal model of laser soldering; The fourth step: Based on the optimal model of laser soldering, perform a feedforward-PI control method; The thermodynamic mathematical model in the second step is: Where ρ is the density of the solder paste, c is the specific heat capacity of the solder paste, P is the laser power, α is the absorption rate, A is the surface area of the solder paste, h is the surface heat transfer coefficient, T is the temperature, t is the time, T0 is the ambient temperature, and V is the volume of the solder paste.

2. A laser soldering modeling and feedforward-PI control method for the model according to claim 1, characterized in that: The most basic mathematical relationship in the first step is: where a is the thermal diffusivity, defined as which is the Laplacian of temperature, is the generalized heat source, ρ is the density of the solder paste, c is the specific heat capacity of the solder paste, and λ is the thermal conductivity coefficient.

3. A laser soldering modeling and feedforward-PI control method for the model according to claim 2, characterized in that: The h, c, and α are obtained by identifying multiple groups of experiments. The process is as follows: Since the surface heat transfer coefficient h and the specific heat capacity c are determined by the properties of the material itself and are independent of whether it is heated or not, substitute the experimental data into the model in the heat dissipation stage to obtain the relevant parameter h / c; Since the state of the solder paste will affect the surface roughness of the surface solder paste and thus affect the absorption rate, substitute the obtained h / c and the experimental data in the heating stage into the thermodynamic mathematical model to find α / h.

4. A laser soldering modeling and feedforward-PI control method for the model according to claim 3, characterized in that: The state of the solder paste will affect the surface roughness of the surface solder paste and thus affect the absorption rate. The heating process of the solder paste is divided into three stages: preheating, melting, and continuous heating after melting. Therefore, the value of α / h needs to be obtained in stages.

5. A laser soldering modeling and feedforward-PI control method for the model according to claim 4, characterized in that: The optimal model of laser soldering in the third step is: where T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, P is the power, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period, and T0 is the ambient temperature.

6. A laser soldering modeling and feedforward-PI control method for the model according to claim 5, characterized in that: In the fourth step, the optimal model of laser soldering is controlled by feedforward-PI. According to the optimal model T(k) and the target function T tar (t), the output power u of the feedforward controller at time k is obtained f (k). Then, according to the deviation value e(k) between the output and the target, the output power u of the PI controller at time k is calculated p (k). The sum of u p (k) and u f (k + 1) is obtained as u(k + 1) and used as the input; Among them T(k) and T(k - 1) are the temperatures at the current moment and the previous moment respectively, P is the power, α / h and h / c are model identification parameters, A is the surface area of the solder paste, m is the mass of the solder paste, T s is the sampling period, T0 is the ambient temperature, where u p (k) is the output power (W) of the PI controller at the k-th moment, u f (k) is the output power (W) of the feedforward controller at the k-th moment, e(k) is the temperature error (°C) during heating at the k-th moment, K P and K I are the proportional coefficient and the integral coefficient respectively.

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