Mathematical calculation method and model for furnace temperature curve of total hot air re-bonding furnace

Abstract

The application provides a full hot air reflow furnace temperature curve mathematical calculation method and model, including the following steps: dividing the full hot air reflow furnace, using a first temperature change calculation model and a second temperature change calculation model to respectively calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow furnace, the temperature change of the circuit board in the gap between each temperature zone of the full hot air reflow furnace, and the temperature change of the circuit board in the rear area of the full hot air reflow furnace; and drawing the furnace temperature curve of the circuit board in the full hot air reflow furnace according to the obtained multiple temperature changes; the application can effectively reduce the artificial test man-hour cost, the manufacturing temperature measurement plate cost and the auxiliary material cost; meanwhile, the best weldability can be obtained through curve prediction, damage to components caused by over-temperature is avoided, and the welding quality is ensured.

Description

Technical Field

[0001] This invention relates to the field of welding in the production of electronic products such as integrated circuit boards, and specifically to a mathematical calculation method and model for the furnace temperature curve of a full hot air reflow oven. Background Technology

[0002] With the increasing integration of microelectronic circuits, surface mount technology (SMT) has technically met the needs of the modern electronics industry, thus its importance in electronic product manufacturing has grown significantly. The reflow soldering process, implemented in a reflow oven, is a crucial process on the SMT production line. It involves heating the circuit board to remelt the solder paste, allowing electronic components to flow with the paste and be automatically soldered onto the circuit board. The temperature control of various parts of the reflow oven directly determines the final quality of the SMT products; therefore, controlling and optimizing the oven temperature profile is essential. Currently, the control and optimization of the oven temperature profile is achieved through experimental testing, which is both time-consuming and costly. Summary of the Invention

[0003] The purpose of this invention is to provide a mathematical calculation method and model for the furnace temperature curve of a full hot air reflow oven, which solves the problem of high cost in existing reflow oven temperature curve control.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] This invention provides a mathematical calculation method for the furnace temperature curve of a full-hot blast reflow furnace, comprising the following steps:

[0006] Step 1: Obtain the temperature calculation model for calculating the circuit board in the front area, back area and each temperature zone gap of the full hot air reflow oven, and obtain the small temperature zone temperature calculation model for calculating the circuit board in each small temperature zone of the full hot air reflow oven.

[0007] Step 2: Discretize the temperature calculation model and the small temperature zone temperature calculation model obtained in Step 1 to obtain the first temperature change calculation model and the second temperature change calculation model.

[0008] Step 3: Calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven, the temperature change of the circuit board between each temperature zone of the full hot air reflow oven, and the temperature change of the circuit board in the rear area of ​​the full hot air reflow oven using the first temperature change calculation model and the second temperature change calculation model, respectively.

[0009] Step 4: Based on the multiple temperature changes obtained in Step 3, plot the furnace temperature curve of the circuit board in the full hot air reflow oven.

[0010] Preferably, in step 1, the expression for the temperature calculation model is:

[0011]

[0012] Where T0 is the initial temperature of the circuit board entering a certain temperature range; T area τ represents the temperature of the small temperature range; t represents time; τ represents the temperature of the small temperature range. r is the thermal time constant.

[0013] Preferably, in step 1, the expression for the temperature calculation model of the small temperature zone is:

[0014]

[0015] Where T0 is the initial temperature of the circuit board entering a certain temperature range; T area t represents the temperature of the small temperature zone; t represents time.

[0016] Preferably, in step 2, the expression for the first temperature change calculation model is:

[0017]

[0018] Among them, T area Temperature for each sub-temperature zone; τ r is the thermal radiation time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0019] Preferably, in step 2, the expression for the second temperature change calculation model is:

[0020]

[0021] Among them, T area Temperature for each sub-temperature zone; τ c is the thermal convection time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0022] Preferably, in step 3, the temperature changes of the circuit board in each small temperature zone of the full hot air reflow oven, the temperature changes of the circuit board between each temperature zone of the full hot air reflow oven, and the temperature changes of the circuit board in the rear area of ​​the full hot air reflow oven are calculated using the first temperature change calculation model and the second temperature change calculation model, respectively. The specific method is as follows:

[0023] S31, Given the initial temperature conditions of the circuit board, and combined with the first temperature change calculation model, the temperature change of the circuit board in the front area of ​​the full hot air reflow oven is calculated.

[0024] S32, update the initial temperature conditions of the circuit board based on the obtained temperature change of the circuit board in the furnace front area, and calculate the temperature change of the circuit board in the first small temperature zone of the heating zone by combining the second temperature change calculation model.

[0025] S33, update the initial temperature conditions using the temperature change of the circuit board in the first small temperature zone of the heating zone, and calculate the temperature change of the circuit board in the gap between the first temperature zones using the first temperature change calculation model.

[0026] S34, update the initial temperature conditions using the temperature changes obtained from the previous region, and calculate the temperature changes of the circuit board in the remaining region by selecting a calculation model based on the applicable conditions of the heat transfer equation.

[0027] A mathematical calculation model for the furnace temperature curve of a full-hot blast reflow oven includes:

[0028] The first temperature change calculation model is used to calculate the temperature change of the circuit board in the front area, the back area and the gap between each temperature zone of the full hot air reflow oven.

[0029] The second temperature change calculation model is used to calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven.

[0030] Curve plotting model; used to plot the furnace temperature curve of a circuit board in a full hot air reflow oven.

[0031] Preferably, the expression for the first temperature change calculation model is:

[0032]

[0033] Among them, T area Temperature for each sub-temperature zone; τ r is the thermal radiation time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0034] Preferably, the expression for the second temperature change calculation model is:

[0035]

[0036] Among them, T area Temperature for each sub-temperature zone; τ cis the thermal convection time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] This invention provides a mathematical calculation method for the temperature curve of a full-hot air reflow oven. Currently, while temperature sensors and other technologies can be used to test and optimize oven temperatures, adjusting for changes in performance indicators through experimental testing is time-consuming and labor-intensive. The calculation method proposed in this invention, by analyzing the heating principle of the full-hot air reflow oven, can theoretically calculate the temperature change curve of the circuit board in ovens with varying heating temperatures, temperature zone lengths, and moving speeds. This method effectively reduces the cost of manual testing, temperature measuring board manufacturing, and auxiliary materials. Simultaneously, it allows for optimal solderability prediction through curve analysis, preventing damage to components due to overheating and ensuring soldering quality. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of a full-hot air reflow furnace divided into 11 small temperature zones;

[0040] Figure 2 It is a temperature distribution map corresponding to each of the 11 sub-temperature zones;

[0041] Figure 3 This is a flowchart illustrating the present invention;

[0042] Figure 4 This is a comparison chart of experimental data and calculated data;

[0043] Figure 5 This is the flowchart of the process. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings.

[0045] Because the full-hot air reflow oven is large in volume, the temperature distribution in each region is different, and the boundary conditions are different, it is impossible to solve the temperature distribution using conventional heat transfer methods. Therefore, this invention mainly proposes a method for solving the circuit board temperature curve under multi-region and multi-boundary conditions.

[0046] Figure 1The demonstration shows a full-heat air reflow oven divided into 11 small temperature zones. The circuit board moves from left to right to complete the soldering process. The first 9 small temperature zones are heating zones, and the last 2 small temperature zones are cooling zones. The heating zone includes a preheating zone, a constant temperature zone, and a reflow zone. The soldering work area of ​​the circuit board is on a conveyor belt. The circuit board is moved through the preheating zone, the constant temperature zone, and the reflow zone by the conveyor belt to complete the soldering.

[0047] Temperature distribution maps for each temperature zone are as follows Figure 2 As shown, it is assumed that the temperature of each small temperature zone is not affected by other temperature zones, and the temperature within the gap is controlled by the two small temperature zones at both ends to form a linear distribution. Under this condition, the boundary conditions are changed.

[0048] like Figure 3 As shown, the present invention provides a mathematical calculation method for the furnace temperature curve of a full hot blast reflow furnace, comprising the following steps:

[0049] Step 1: Obtain the temperature calculation model for calculating the temperature change of the circuit board in the front area, back area and between each temperature zone of the full hot air reflow oven, as well as the small temperature zone temperature calculation model for the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven.

[0050] The temperature zone gap refers to the gap between two adjacent small temperature zones in the heating zone.

[0051] Step 2: Discretize the temperature calculation model and the small temperature zone temperature calculation model obtained in Step 1 to obtain the first temperature change calculation model and the second temperature change calculation model.

[0052] Step 3: Given the initial temperature conditions of the circuit board, and combined with the first temperature change calculation model, calculate the temperature change of the circuit board in the front area of ​​the full hot air reflow oven.

[0053] Step 4: Update the initial temperature conditions of the circuit board based on the temperature of the circuit board in the previous area. According to the applicable conditions of the heat transfer equation, calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven, the temperature change of the circuit board in the gap between each temperature zone of the full hot air reflow oven, and the temperature change of the circuit board in the rear area of ​​the full hot air reflow oven using the first temperature change calculation model and the second temperature change calculation model respectively.

[0054] Step 5: Based on the multiple temperature changes obtained in Step 3 and Step 4, plot the furnace temperature curve of the circuit board in the full hot air reflow oven.

[0055] Specifically, the present invention provides a mathematical calculation method for the furnace temperature curve of a full hot blast reflow furnace, comprising the following steps:

[0056] Step 1: Based on the working process and design of the hot air reflow oven to be tested, the heat transfer mode of each small temperature zone in the reflow oven is set as thermal convection. According to Newton's law of cooling, the convective heat transfer per unit area of ​​the small temperature zone, q, can be obtained. c :

[0057] q c =h c (T area -T) (1)

[0058] Where, q c The convective heat transfer per unit area in each small temperature zone; T area Temperature for each small temperature zone; T is the temperature of the circuit board; h c The convective heat transfer coefficient can be determined by the length of the circuit board and its thermal conductivity.

[0059] There is no special temperature control in the furnace front area, furnace rear area, and temperature zone gaps. Heat is mainly absorbed from adjacent smaller temperature zones through thermal radiation. Therefore, based on the thermal radiation heat transfer formula, the corresponding thermal radiation heat transfer Q for the furnace front area, furnace rear area, and temperature zone gaps can be obtained respectively:

[0060]

[0061] Where σ is the blackbody radiation constant, σ = 5.67 × 10⁻⁶ -8 W / (m 2 ·K 4 A is the area of ​​the circuit board, ε1 is the emission coefficient at a point on the furnace wall, and ε2 is the emission coefficient at any point on the soldering area of ​​the circuit board.

[0062] Based on the obtained heat transfer through radiation, a unified heat transfer equation is established corresponding to the circuit board. The unified heat transfer equation for the circuit board is the radiation heat transfer equation q per unit area of ​​the circuit board. r :

[0063]

[0064] q r =h r (T area -T) (4)

[0065] Among them, h r The radiative heat transfer coefficient is...

[0066] Replace T in the equation with the average temperature of the circuit board in the current region, so that h r It then became a and h c Similar constants.

[0067] Step 2: Based on the law of conservation of energy and Fourier's law, obtain the convective heat transfer differential equation corresponding to the circuit board:

[0068]

[0069] Where T is the temperature of the circuit board; t is time; ρ is the density of the circuit board; and c p The specific heat capacity at constant pressure of hot air; The heat generated by the internal heat source represents the heat generated by the internal heat source per unit volume per unit time.

[0070] Equations (1) and (5) are combined to eliminate the heat parameter. The differential equation of the circuit board with respect to temperature in the small temperature range is obtained as follows:

[0071]

[0072] Among them, T area A is the temperature of the small temperature zone; A is the area of ​​the circuit board; V is the volume of the circuit board.

[0073] In the heat transfer convection region (small temperature range), the initial temperature conditions for the circuit board are set as follows:

[0074] T(0) = T0

[0075] Where T0 is the initial temperature of the circuit board entering a certain small temperature zone;

[0076] Integrating equation (6) based on the initial temperature condition yields an expression for the temperature change of the circuit board over time in any small temperature zone. This expression is then used as the temperature calculation model for the small temperature zone.

[0077]

[0078] in, τ c T is the thermal convection time constant, which reflects the response rate of the heated object's temperature to the heat source temperature; T(t) is the temperature of the circuit board at time t.

[0079] Similarly, the differential equation for temperature of the circuit board in the thermal radiation heat transfer region (front of the furnace, rear of the furnace, or temperature zone gap) is as follows:

[0080]

[0081] Within the heat radiation transfer zone (furnace front zone, furnace rear zone, or temperature zone gap), the initial temperature conditions for the circuit board are set as follows:

[0082] T(0) = T0

[0083] Wherein, T0 is the initial temperature corresponding to the circuit board entering the furnace front area, furnace back area, or temperature zone gap;

[0084] Based on the initial temperature condition, integrating equation (8) yields an expression for the temperature change of the circuit board over time in the furnace front region, furnace back region, or temperature zone gap. This expression is used as the temperature calculation model.

[0085]

[0086] Where, τ r The thermal radiation time constant, T(t) represents the temperature of the circuit board at time t.

[0087] Step 3: Discretize the obtained small-temperature zone temperature calculation model and temperature calculation model respectively to obtain the second temperature change calculation model and the first temperature change calculation model. Specifically:

[0088] First, set the discretization time interval.

[0089] Discretization time interval is set according to conveyor belt speed. Among them, t all The time required to traverse a certain continuous region. l is the length of the area; v is the speed of the conveyor belt.

[0090] Secondly, based on the set discretization time interval, equations (7) and (9) are transformed into difference forms to obtain the second temperature change calculation model (11) and the first temperature change calculation model (10), respectively:

[0091]

[0092]

[0093] Where T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals.

[0094] Step 5: Calculate the furnace temperature profile of the circuit board in the hot air reflow oven based on the circuit board manufacturing process.

[0095] First, the initial temperature condition of the circuit board is given as T(0) = T room , among which, T room This refers to the temperature of the area where the circuit board is currently located.

[0096] Secondly, the temperature change of the circuit board in the furnace front area is calculated by combining the initial temperature conditions of the circuit board with Equation (10);

[0097] Next, the initial temperature conditions of the circuit board are updated using the temperature change of the circuit board in the furnace front area, and the temperature change of the circuit board in the first small temperature zone of the heating zone is calculated by combining equation (11).

[0098] Next, the initial temperature conditions are updated using the temperature change of the circuit board in the first small temperature zone of the heating zone, and the temperature change of the circuit board in the first temperature zone gap is calculated using Equation (10).

[0099] Next, the initial temperature conditions are updated using the temperature changes obtained from the previous region, and the temperature changes of the circuit board in the remaining region are calculated based on the applicable conditions of the heat transfer equation and the calculation model.

[0100] Finally, the obtained temperature changes are plotted to obtain the furnace temperature curve of the circuit board in the full hot air reflow oven.

[0101] like Figure 5 As shown, the present invention also provides a mathematical calculation model for the furnace temperature curve of a full hot blast reflow furnace, including:

[0102] The first temperature change calculation model is used to calculate the temperature change of the circuit board in the front area, the back area and the gap between each temperature zone of the full hot air reflow oven.

[0103] The second temperature change calculation model is used to calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven.

[0104] Curve plotting model; used to plot the furnace temperature curve of a circuit board in a full hot air reflow oven.

[0105] The expression for the first temperature change calculation model is:

[0106]

[0107] Among them, T area Temperature for each sub-temperature zone; τ r is the thermal radiation time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0108] The expression for the second temperature change calculation model is:

[0109]

[0110] Among them, T area Temperature for each sub-temperature zone; τ cis the thermal convection time constant; T(i) is the temperature of the circuit board in the i-th discretization time interval in the furnace front area; i is the number of discretization time intervals; T(i+1) is the temperature of the circuit board in the (i+1)-th discretization time interval in the furnace front area.

[0111] To evaluate the accuracy and practicality of the calculation model, calculations were performed on a reflow oven with 11 small temperature zones, a front zone, and a rear zone. Each small temperature zone is 30.5 cm long, with a 5 cm gap between adjacent zones. The front and rear zones are both 25 cm long. The conveyor belt speed is 78 cm / min, and the setpoints for each temperature zone are as follows: (Small Temperature Zones 1-5) (Small Temperature Zone 6) (Small Temperature Zone 7) and (In the small temperature zone 8-9), the furnace temperature curve was plotted using the calculation model proposed in this invention, and compared with the experimental data, as follows: Figure 4 As shown, the two are basically consistent, verifying the practicality and reliability of the calculation model.

Claims

1. A mathematical calculation method for the furnace temperature curve of a full-hot blast reflow furnace, characterized in that, Includes the following steps: Step 1: Obtain the temperature calculation model for calculating the circuit board in the front area, back area and each temperature zone gap of the full hot air reflow oven, and obtain the small temperature zone temperature calculation model for calculating the circuit board in each small temperature zone of the full hot air reflow oven. Step 2: Discretize the temperature calculation model and the small temperature zone temperature calculation model obtained in Step 1 to obtain the first temperature change calculation model and the second temperature change calculation model. Step 3: Calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven, the temperature change of the circuit board between each temperature zone of the full hot air reflow oven, and the temperature change of the circuit board in the rear area of ​​the full hot air reflow oven using the first temperature change calculation model and the second temperature change calculation model, respectively. Step 4: Based on the multiple temperature changes obtained in Step 3, plot the furnace temperature curve of the circuit board in the full hot air reflow oven; The expression for the temperature calculation model in Step 1 is as follows: in, The initial temperature at which the circuit board enters a certain temperature range; The temperature of the small temperature zone; t For time; The thermal time constant; ; A The area of ​​the circuit board; V This refers to the volume of the circuit board; The density of the circuit board; The specific heat capacity at constant pressure of hot air; The radiative heat transfer coefficient is used; in step 1, the expression for the temperature calculation model in the small temperature zone is: in, The initial temperature at which the circuit board enters a certain temperature range; The temperature of the small temperature zone; t For time; , The thermal time constant for heat convection; The convective heat transfer coefficient is given.

2. The mathematical calculation method for the furnace temperature curve of a full-hot blast reflow furnace according to claim 1, characterized in that, In step 2, the expression for the first temperature change calculation model is: in, Temperature for each small temperature zone; The thermal radiation time constant; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The number of discretization time intervals; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The time interval is for discretization.

3. The mathematical calculation method for the furnace temperature curve of a full-hot blast reflow furnace according to claim 1, characterized in that, In step 2, the expression for the second temperature change calculation model is: in, Temperature for each small temperature zone; The thermal time constant for heat convection; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The number of discretization time intervals; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The time interval is for discretization.

4. The mathematical calculation method for the furnace temperature curve of a full-hot blast reflow furnace according to claim 1, characterized in that, In step 3, the temperature changes of the circuit board in each small temperature zone of the full hot air reflow oven, the temperature changes of the circuit board between each temperature zone of the full hot air reflow oven, and the temperature changes of the circuit board in the rear area of ​​the full hot air reflow oven are calculated using the first temperature change calculation model and the second temperature change calculation model, respectively. The specific method is as follows: S31, Given the initial temperature conditions of the circuit board, and combined with the first temperature change calculation model, the temperature change of the circuit board in the front area of ​​the full hot air reflow oven is calculated. S32, update the initial temperature conditions of the circuit board based on the obtained temperature change of the circuit board in the furnace front area, and calculate the temperature change of the circuit board in the first small temperature zone of the heating zone by combining the second temperature change calculation model. S33, update the initial temperature conditions using the temperature change of the circuit board in the first small temperature zone of the heating zone, and calculate the temperature change of the circuit board in the gap between the first temperature zones using the first temperature change calculation model. S34, update the initial temperature conditions using the temperature changes obtained from the previous region, and calculate the temperature changes of the circuit board in the remaining region by selecting a calculation model based on the applicable conditions of the heat transfer equation.

5. A mathematical calculation system for the furnace temperature curve of a full-hot blast reflow oven, characterized in that, include: The first temperature change calculation model is used to calculate the temperature change of the circuit board in the front area, the back area and the gap between each temperature zone of the full hot air reflow oven. The second temperature change calculation model is used to calculate the temperature change of the circuit board in each small temperature zone of the full hot air reflow oven. Curve drawing model; Used to plot the furnace temperature profile of the circuit board in a full hot air reflow oven; the expression for the first temperature change calculation model is: in, Temperature for each small temperature zone; The thermal radiation time constant; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The number of discretization time intervals; For the circuit board in the furnace front area The temperature corresponding to each discretized time interval; the expression for the second temperature change calculation model is: in, Temperature for each small temperature zone; The thermal time constant for heat convection; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The number of discretization time intervals; For the circuit board in the furnace front area Temperature corresponding to each discrete time interval; The time interval is for discretization.

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