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The Thermal Profile of a No. 10 Soldering Iron: A Software Solution Design Team 3 Bryan Douglas Mike Tetreault Kristine McCarthy Monday, February 13, 2006 Objectives: Research different types of temperature sensors Find a J-type thermocouple to use for testing Create the Thermal profile using Excel and test results Create a program in VEE to find a solution to the thermal profile Mathematically model the thermal profile of any new soldering iron Discussion of Theory: Basic Information on J-Type Thermocouples: Thermocouples are a device used for measuring temperature. They are consisted of two different types of metals welded together at a point. One metal is specified as the positive end and the other wire is the negative. Thermocouples consist of many different types, each using different metals for each. A J-type thermocouple contains an iron wire for the positive end which is wrapped in a white casing and a constantan wire for the negative which is wrapped in a red casing. To determine the positive, or iron wire, the thermocouple can be connected to a dmm and if the reading is positive then the positive lead is on the iron wire and if the reading is negative then iron wire is on the negative lead. Once the iron wire is found the constantan is the other wire on the thermocouple. Cold Junction Compensation: The measuring junction is the welded part of the thermocouple that is heated to create a Seebeck voltage. The two separated ends of the thermocouple are connected to the leads of the dmm and this is known as the reference junction. When the leads are connected to a thermocouple two additional thermocouples 2 are created. This is known as the cold junction. To compensate for this, the cold junction can be placed in an ice bath but since this is not practical, the voltage of the room is simply taken into account and subtracted from the voltage reading on the dmm as shown in equation (1). This is better known as cold junction compensation. For example, if the reference junction temperature was at 25 ºC, and the Seebeck voltage was measured at 3.991 mV, with the cold junction compensation taken into consideration, the temperature would be 76 ºC. VCORRECTED VM VR VC (1) Measuring Temperature with A Thermocouple: When the measuring junction of the thermocouple is heated, a thermoelectric voltage is created. This voltage is known as Seebeck voltage. To convert the voltage manually, the output voltages can be compared to a thermoelectric table that shows the temperature values that coincide with the measured voltages. This can also be verified by equation (2): change in voltage equals the Seebeck voltage times the change in temperature. V VSEEBECK T (2) 3 Vr + Vm DMM HI LO Figure-1 Basic Laboratory Setup Definition of Design Problem: The objective was to design a computer based data acquisition system to sense the tip temperature of a standard Number 10 soldiering iron and then display the resulting thermal profile graphically on a computer. In order to accomplish this task, knowledge of the specifications of the soldiering iron was required. Since the exact temperature specifications were not known, educated guesses were made that TMAX 400º C , TMIN 20C and the required time for the iron to achieve operating temperature is between five and ten minutes. It was also predicted that the thermo profile would show a rapid initial temperature rise and then would show a slower rise as the iron neared adequate operating temperature. As for the sensor, it was decided that the accuracy should be within 1% of the predicted operating temperature, or ± 4 ºC and that the response time would be acceptable at about 1 second. The price was then set at $10 or less. Additionally, the sensor size would be very important. If the sensor was too big, it would cause the results to be greatly skewed due to the fact that the time it took to heat up the sensor would also be 4 taken into account. Therefore the size of the sensor should not exceed .025in x .025in since the soldering iron tip is .25in x .25in. Formulate a voltage-to-temperature conversion equation: Knowing that the voltage from the DMM could be used to get a voltage reading from the thermocouple, that voltage needed to be converted to a temperature to become useful. To find the best possible equation with the least amount of error it was necessary to test multiple equations to ensure minimal error. The voltage and temperature from Table 1was recorded every ten degrees Celsius up to five hundred degrees. This voltage from Table 1 was input as (Vm) and the temperature was input as Tc. The Vm and Tc were graphed in Excel as shown in Figure 6, Vm being the independent variable and Tc being the dependent variable. A trend line was added in Excel and an equation for the line of best fit was developed by Excel. This provided the formula for the voltage-totemperature equation giving Tm or temperature measured. Tm was then subtracted by Tc to find the residue which is the amount of error that varied from Table 1. The residue was then added together and showed how much the data deviated from Table 1, providing the error of the equation. This process was used for the graphs of the linear function, power function, and polynomial functions 2, 3, and 4. After computing all of the different functions, the 4th order polynomial had the least amount error with a residue of 1.363 shown in Equation (3). Figure 4 displays the graph of the polynomial 4 with the conversion equation. This formula is the equation that will be used to convert the voltage-to-temperature because it had the least amount of error. Tm = -111386012 (Vm)4 + 7388878 (Vm)3 - 170717 (Vm)2 + 19668 (Vm) + 0.1 Residue = 1.363976397 (3) 5 Polynomial 4 Conversion Equation 600 500 Tm = -111386012.987305000000(Vm)4 + 7388878.258422850000(Vm)3 - 170717.226848602000(Vm)2 + 19668.352335084200(Vm) + 0.108963724946 R2 = 0.999999951873 400 Tm (oC) 300 200 100 0 0 0.005 0.01 0.015 Vm (Volts) 0.02 0.025 0.03 Figure 4 – Polynomial 4 Conversion Equation 6 Table 1 – Thermoelectric Table 7 The thermal profile of a soldering iron taken manually: Once the equation to convert the voltage form the thermocouple to a temperature was completed, the next step was to physically test the soldering iron and see the limitations of the unit. A J-type thermocouple was chosen because it met all of the specifications needed. A sample of the thermocouple was acquired and then the diameter of the end which was going to measure the temperature of the iron was measured. It was measured with a micrometer and once the diameter was determined a drill bill onethousandth bigger was selected. A jig was build to hold the soldering iron as the tip was drilled half way through with a drill press. After being drilled, the thermocouple was pressed fitted into the soldering iron and ready for testing. After the thermocouple was attached to the 25-watt soldering iron, we hooked the leads on the thermocouple up to the dmm. The white, or positive, end of the thermocouple was hooked up to the positive terminal of the dmm and the red, or negative, end was hooked up to the negative terminal of the dmm. Once we insured our connections were correct and connected well we created an Excel spreadsheet of time versus temperature. Every fifteen seconds a reading was taken manually from the mulitmeter until the soldering iron reached thermal equilibrium. From this, the maximum temperature of the soldering iron and how long it took to reach operating temperature could be determined. Finally, the soldering iron was plugged into the wall and the process of recording the voltage from the dmm every fifteen seconds began. Once all of the measurements were taken, we the results were plugged into the voltage-to-temperature equation in order 8 to convert the recorded data to temperature and find the thermal equilibrium point. At around eighteen to twenty minutes and 362 °C, the soldering iron appeared that it had reached thermal equilibrium as shown in figure 3. The graph was an exponential graph that quickly rose in temperature from zero to around eight minutes and then began to level off. From the obtained data, we now had the shape of the graph, maximum temperature, and amount of time it took for the soldering iron to reach thermal equilibrium. The baselines could now be used in the computer program to accurately measure the thermal profile of the soldering iron to eliminate the human error. Thermal Profile 400 350 300 Temperature (oC) 250 200 150 100 50 0 0 5 10 Time (minutes) 15 20 25 Figure 3 – Approximated Thermal Profile of Soldering Iron The final VEE Pro 6.0 software development: 9 The final solution to for the temperature sensing by the thermocouple and displaying the results in a program designed in VEE 6.0. This program takes away the long process of correcting the cold junction and almost eliminates human error. The program starts with a For Count and a Delay. The For Count controls the amount of measurements taken and the Delay controls how often each measurement is taken. By multiplying the For Count by the Delay you can calculate the amount of seconds the program takes measurements for and then by dividing by 60 the user can calculate the minutes it runs for. After the For Count and Delay are configured, the dmm is turned on and hooked up to the soldering iron and a new Excel spreadsheet is open the program can be run (Excel must be open because data is exported from VEE to Excel). To run the program the user hits the forward or play arrow in the middle of the toolbar. Once that button is hit it starts the For Count. The Delay then sends 2 pinges; one to a counter and the other to the dmm once the time in the Delay is up. The pinge sent to the dmm then takes a reading in volts out of the dmm and sends it to equation (2) which compensates for the cold junction. The voltage is then sent to a collector where it is stored until the program finishes running. Once the For Count finishes, a pinge is sent form the For Count to the Collector which then sends each of the voltages to a formula which then converts the voltage to a temperature in Celsius and is then sent to a graph in VEE and the exported data sheet in Excel. That data is also sent to another formula box which converts the degrees in Celsius to degrees Fahrenheit and also displays the temperature versus time on a graph. 10 The time was acquired when each pinge from the Delay was sent to a counter. The counter counted each time a pinge was sent to it and then sent that number to equation (3) which converted that number to time in seconds. That time was then sent to a collector and stored until the program finished. Once the program finishes a pinge from the For Count is sent to the collector which releases each time interval to the two graphs and to a data collector which then exports the data to the Excel spreadsheet. The graphs used the time in the graph to plot temperature vs. time. (Output Delay) 60 = Seconds (3) By using the developed software, a user can hook up the thermocouple to the dmm and take measurements via the computer. This eliminates the chance for human error. The software when run will record the data of the soldering iron being heated and then display the thermal profile of the soldering iron graphically. The graphs will display ºC and ºF versus time and the data will also be exported to Excel which can later be graphed in Excel. In addition to what is pictured in Figure 3, there are two Notepad windows in which contain information for the user. The first explains what the program does with the current settings and the process it goes through to get the information that it outputs. The second explains how to change the settings to work with the particular make and model of soldering iron that the user is testing. 11 Figure 2 – Schematic of VEE Program Modeling the thermal profile of a № 10 Soldering Iron mathematically: In the mathematical model of the soldering iron two different polynomials were used to model any kind of new soldering iron that will be made in the future. Using the thermal profile (Figure 3), a trend line was added to the data. The trend line is a third order polynomial. Since splitting up the data would be the best approach, a breakpoint was chosen to split the thermal profile into two sections. The breakpoint of this data was chosen to be 383. Any number under 383 in the data range would be modeled into the first part of the profile which is a 2nd order polynomial with equation (4), and any number above 383 would be in the second part of the profile. The second part of the thermal profile is also a 2nd order polynomial with equation (5). The model of the two equations placed together produced a reasonable model, but a hole appeared where the two equations joined each other at the breakpoint. To fix this problem, the data from the 12 second half of the profile was extended to overlap the first equation of the profile to blend the two polynomials together. Tm = -0.0017 * Vm² + 1.486 * Vm +11.854 Tm = -0.0002 * Vm² + 0.304 *Vm +241.12 A mathematical model is useful to have because it will be capable of predicting the performance of any new soldering iron before it is built, saving time and money. Conclusion: After all research was done, tests completed, programs written, formulas and results verified, and data and graphs scrutinizes and revised, it was decided that the preceding design was the best solution to the problem. The program covers all the required elements of the design and provides a user-friendly operation. The program measures the input voltage and computes this voltage to give you the desired outputs of temperature and time. You simply need to know two things: the desired number of measurements to be taken and the interval at which this is to be done. All of the components of this solution were chosen or designed with specific intentions in mind. For example, the J-Type thermocouple was chosen because it had the required sensing range, and was within the size, sensitivity, and accuracy limits. Also, the temperature conversion equation had to be chosen from a few different possibilities. The decision had to be made whether to use the equation from a linear, power, or 2nd 3rd or 4th order polynomial graphs. It was only chosen after further calculations of the square of the residue (R2) and seeing which value was closest to 1. This gave us the most accurate results. Additionally, the VEE program had to be absolutely perfect. Many trial runs were made and many versions were created before one was made that produced the desired (4) (5) 13 output of temperature vs. time graphs and exported the results into an Excel spreadsheet for further review. Of course, our results had to be verified. First, we had to verify the voltage-totemperature conversion equation. It was checked and rechecked and no fault was found. Then there was the verification of the data. The initial temperature, of course, was simply verified by checking the room temperature which was measured at 24.6 ºC by the thermocouple which is approximately average room temperature. As for the final temperature, the predicted maximum temperature was 400 ºC so the measured final temperature of 377.8 ºC is a reasonable account. Any difficulties experienced in the development of our solution were only minor setbacks. When writing the VEE program, one of the biggest problems that we encountered was calibrating the input the time correctly into the graphs. Another problem was synchronizing the entire program. A few different methods were tried including alphanumeric data loggers, but once a collector was added into both the time and voltage lines, the program ran smoothly and correctly. We also experienced difficulty with the mathematical model of the thermal profile. The error in the graph was that where the two lines of the equations met, there was a jump. All of the combinations possible were tried, and the one with the smallest jump was the 2nd order polynomial to 2nd order polynomial graph. This discrepancy was worked on for some time and finally it was remedied by reworking the equations. As shown in Figure 2, the initial objective of displaying the thermal profile graphically, exporting the data to Excel, and making a mathematical model were accomplished. The VEE program measured the voltage, passed it through the conversion 14 equation and then to a data collector. The collector then stored the information until a pinge telling it to input the information into the graphs of temperature vs. time and ultimately into the Excel spreadsheet. This allowed the mathematical model of the thermal profile to be made. 15