MIT2_007s09_lec12_note

MIT2_007s09_lec12_note - MIT OpenCourseWare...

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MIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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2.007 –Design and Manufacturing I Gears: T erminology, Geometry, Gear Trains, Strength Presented by Dan Frey on 17 MAR 2009 Images from Wikimedia Commons, http://commons.wikimedia.org
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Today’s Agenda • Distribute homework #3 •G e a r s – Applications – Types – Terminology / nomenclature – Congugate action – Involute curve – Analysis & design
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Applications of Gears Sobel, Dava, Longitude Images removed due to copyright restrictions. Please see http://mossmotors.com/Graphics/Products/Schematics/SPM-027.gif http://www.nmm.ac.uk/collections/displayRepro.cfm?reproID=A6263
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Spur Gears • Transmit motion between parallel shafts • Teeth are parallel to the axis of rotation • This is the simplest kind of gear we’ll consider and most of today is dedicated to them
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Gear Terminology Diametral pitch (teeth per inch) # of teeth on a gear with a 1 inch pitch diameter Easily confused Source: Fig. 1.1 in “Gears.” Design and Application of Small Standardized components Data Book 757 . Stock Drive Products, 1983. Accessed September 18, 2009. Courtesy of Stock Drive Products/Sterling Instrument.
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Other Types of Gears Helical Bevel Rack Worm Courtesy OSHA. Images from Wikimedia Commons, http://commons.wikimedia.org Image courtesy of perlmonger on Flickr.
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Early Gears Roman watermills at Barbegal 300AD Application for powering textile machinery 18 th century Drawings of waterwheels and gears removed due to copyright restrictions.
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Conjugate Action ω Α A B ω Β Let’s say ω A is a known. How can we determine ω B ? Let’s say ω A is a constant with time. Can we synthesize a shape of body B so that ω B is also constant with time? NOTE: As discussed in class, the rotation of the driven body B can be inferred. The key is that the two bodies stay in contact even after a small increment of rotation. For this reason, the “gear ratio” is a function of the orientation of the line normal to the point of contact. Yes, generally one can synthesize a shape B for any shape A to attain conjugate action. An analog of a “rack cutting” procedure would generally do it.
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Point ω Α A B ω Β What is the pitch point? What is the line of action? What are the relationships among these? Pitch point (p). The point where the line of action crosses a line joining the two gear axes. Line of action , also called ' Pressure line' . The line along which the force between two meshing gear teeth is directed. It has the same direction as the force vector. In general, the line of action changes from moment to moment during the period of engagement of a pair of teeth. For involute gears, however, the tooth-to-tooth force is always directed along the same line -- that is, the line of action is constant. this implies that for involute gears the path of contact is also a straight line, coincident with the line of action -- as is indeed the case. http://en.wikipedia.org/wiki/Gear
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MIT2_007s09_lec12_note - MIT OpenCourseWare...

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