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SEPTEMBER 2022 I SMT007 MAGAZINE 81 "Ugh, line balancing," he groaned. "Well, what is usually the 'gate' in electronic assembly?" Sue asked, as Andy responded, "Component placement." "So, say we have two component placement machines, a chip shooter and a flexible placer," Sue began. "e chip shooter takes 35 seconds to place all of the passive 'chips' and the flex- ible placer takes 25 seconds to place the sim- ple integrated circuits (SICs) and the complex integrated circuits (CICs). What should we do?" "Move passives to the flexible placer," Andy responded. "But how many passives?" Sue teased. "at's where I get stuck," he admitted. "Well, we want the time on each placement machine to be the same, right?" Sue queried. "Okay, so we take the passives off the chip shooter and that speeds it up and adds the pas- sives to the flexible placer that slows it down," Andy said, his voice rising in excitement. "We want to do this so that the times are the same. Now we need a math equation. Let me see if I can set it up." Sue commented, "Well, we need to know the numbers of components and placement speeds. Let's assume there are 350 passives, 28 SICs, and six CICs. Also, that the chip shooter places passives at 30,000 per hour, and the flexible placer places passives and SICs at 8,000 per hour and complex ICs at 3,000 per hour." "Okay, so the chip shooter takes 350/30,000 = 0.01667 hours to place the passives and the flexible placer takes 28/8000 + 6/3000 = 0.0035 + 0.002 = 0.0055 hours," Andy added. "So, we are waiting on the chip shooter." "Can you set up the equation to determine how many passives need to go to the flexible placer to time balance the line?" Sue asked. Andy responded: "I think so. It would be: (350 – x)/30,000 = 0.0055 + x/8000. e le side of the equation is the time that the chip shooter takes with x less passives and the right side of the equation is the time the flex- ible placer takes to place the integrated circuits and x passives. To be time balanced, the times must be equal. All we have to do is solve for x." With a little manipulation of the equation and their calculators, they solved the equa- tion that x must be equal to 39 passives. So, the time for each machine is (350 – 39)/30,000 = 0.01037 hours or 37.3 seconds. ey discussed a few more things about the workshop on component placement and called it an evening. Epilogue Andy Connors and his dad, Frank, were never very close. Let's listen in on them while they have a little chat. "You know, son, I have never really talked to you much about life or your plans, but I have to tell you, Mom and I are extremely impressed with the change that has come over you recently," Frank said proudly. "Even your boss, Maggie Benson, called us to tell us how proud of you we should be." "Wow, thanks, dad," Andy said. "I think a lot of my motivation has come from knowing Sue March. She is so smart, especially at math." "Well, you know a guy could live 100 life- times and never meet a gal like her—don't lose her," Frank replied. Both Andy and his dad felt a closeness like never before. SMT007 Ronald C. Lasky is an instructional professor of engineering for the Thayer School of Engineering at Dartmouth College, and senior technologist at Indium Corporation. To read past columns, click here. Download The Printed Circuit Assembler's Guide to… Solder Defects by Christopher Nash and Dr. Ronald C. Lasky. You can also view other titles in our full I-007e book library here.