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Seventeen-year-old Ramona, like many of her friends, was bored with school--with books, with classes, and especially with mathematics. So she jumped at the opportunity to enter an apprenticeship program in which she spent half of every week working in a local machine tool shop. Here she would learn to use lathes and drill presses to make useful things, rather than wasting time on math problems that had no earthly purpose that she could discern.

One month after beginning the apprenticeship program Ramona had to set up a computer-controlled lathe to make a ring for a shaft that had been brought in for repair. First she checked the cutting tool to be sure that it was set for the required 15 degree angle. Then she identified the line in the computer code where the lathe would make its first cut on the circumference. She edited the code to include an offset of 5 mils (0.005"). She then executed the code and checked the gap with a 5 mil shim. If the fit was too loose, she corrected the offset and repeated the process. When the machine stopped within the required tolerance, she reset the x coordinate of home by the difference between the thickness of the shim and the amount of the offset. She then repeated the process to reset the y coordinate, made one last check with the 5 mil shim and started the lathe.

The next day, working with the automated drill press on a custom-designed fixture, she checked her set-up by executing the computer code in single-step mode. The drill holes were positioned perfectly on the first side, but after she flipped the fixture over, the holes were obviously way off. She found the line in the code responsible for this step, studied the print-out of the program near this line, and compared it with the earlier section of the program where the drill had worked perfectly. She quickly discovered that the programmer had copied the x and y coordinates from the first part of the program, even though the parts would not be in the same position when the fixture was flipped over. So she edited the program at the computer console, ran the program in single-step mode to ensure that it would work as desired, and then executed a full run. Finally, she notified the programmer of the error she had discovered, and requested that a revised program be installed in the drill.


Excerpted from "Mathematics for Work and Life" by Susan L. Forman and Lynn Arthur Steen (in Seventy-Five Years of Progress: Prospects for School Mathematics, NCTM, 1995).




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Last Update: 12/29/98