MIT2_72s09_lec12

MIT2_72s09_lec12 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 2.72 Elements of Mechanical Design Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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2.72 Elements of Mechanical Design Lecture 1 2 : Belt, friction, gear drives
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chedule and reading assignment Quiz ± Bolted joint qualifying Thursday March 19 th Topics ± Belts ± Friction drives ± Gear kinematics Reading assignment Read: 14.1 – 14.7 Skim: Rest of Ch. 14 © Martin Culpepper, All rights reserved 2
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3 © Martin Culpepper, All rights reserved Topic 1: Belt Drives
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elt Drives Why Belts? ± Torque/speed conversion ± Cheap, easy to design ± Easy maintenance ± Elasticity can provide damping, shock absorption Image by dtwright on Flickr. Keep in mind ± Speeds generally 2500-6500 ft/min ± Performance decreases with age Image by v6stang on Flickr. © Martin Culpepper, All rights reserved 4 Images removed due to copyright restrictions. Please see: http://www.tejasthumpcycles.com/Parts/primaryclutch/3.35-inch-harley-Street-Belt-Drive.jpg http://www.al-jazirah.com.sa/cars/topics/serpentine_belt.jpg
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elt Construction and Profiles Many flavors ± Flat is cheapest, natural clutch ± Vee allows higher torques ± Synchronous for timing Usually composite structure ± Rubber/synthetic surface for friction ± Steel cords for tensile strength © Martin Culpepper, All rights reserved 5
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elt Drive Geometry Driven Slack Side Tight Side Driving Pulley Pulley ω 1 ω 2 d 1 d 2 v belt © Martin Culpepper, All rights reserved 6
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elt Drive Geometry θ 1 θ 2 d span d center © Martin Culpepper, All rights reserved 7
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ontact Angle Geometry θ 1 θ 2 d span d center ω 1 ω 2 d 1 d 2 θ 1 =π − 2sin 1 d 2 d 1 2 =π + 2sin 1 d 2 d 1 2 d center 2 d center © Martin Culpepper, All rights reserved 8
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elt Geometry θ 1 θ 2 d span d center ω 1 ω 2 d 1 d 2 2 2 1 d = 2 2 1 2 ( d 1 θ 1 + d 2 2 ) 4 d center ( d 2 d 1 ) + span d center d d 2 L belt = 2 © Martin Culpepper, All rights reserved 9
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rive Kinematics θ 1 θ 2 d span d center ω 1 ω 2 d 1 d 2 v b = d 2 1 ω 1 = d 2 2 2 d 1 = 2 d 2 1 © Martin Culpepper, All rights reserved 10
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lastomechanics Elastomechanics torque transmission ± Kinematics speed transmission Link belt preload to torque transmission ± Proceeding analysis is for flat/round belt Driven Slack Side Tight Side Driving Pulley Pulley ω 1 ω 2 d 1 d 2 v belt © Martin Culpepper, All rights reserved 11
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ree Body Diagram y x dS F F+dF d θ dN μ dN d/2 •Tensile force (F) •Normal force (N) •Friction force ( μ N) •Centrifugal force (S) © Martin Culpepper, All rights reserved 12
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orce Balance d/2 d θ dN μ dN F Using small angle approx: F+dF Σ F y = 0 = ( F + dF ) d θ F d + dN + dS 2 2 Fd θ= dN + dS Σ F x = 0 = −μ dN F + ( F + dF ) μ dN = dF y dS x © Martin Culpepper, All rights reserved 13
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btaining Differential Eq d/2 d θ dN μ dN F Let m be belt mass/unit length F+dF dS = m d 2 ω 2 d θ 2 Combining these red
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.72 taught by Professor Martinculpepper during the Spring '09 term at MIT.

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MIT2_72s09_lec12 - MIT OpenCourseWare http:/ocw.mit.edu...

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