2.007 –Design and Manufacturing I Gears: Terminology, Geometry, Gear Trains, Strength Today’s AgendaApplications of GearsSpur GearsGear TerminologyOther Types of GearsEarly GearsConjugate ActionPitch PointSliding and RollingRack CuttingInvolute ProfileMore Gear TerminologyPressure LineGear TerminologyPressure AngleConcept QuestionContact RatioInterferenceBacklashGear SelectionWays Gears FailStress in GearsA Beam in BendingConcept QuestionStrength of GearsThe Lewis FormulaOr Use a Canned ToolDiscussion QuestionsConcept QuestionContact Stress (Hertzian Stress) Contact Stress Quantitative CharacterizationSimple Gear TrainsCompound Gear TrainsManual TransmissionsDiscussion QuestionsConcept QuestionDiscussion QuestionsDifferentialsNext StepsPlanetary Gear TrainsAnalysis of Planetary Gear TrainsName That GearFollow upMIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing ISpring 2009For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.2.007 –Design and Manufacturing I Gears: Terminology, Geometry, Gear Trains, Strength Presented by Dan Frey on 17 MAR 2009Images from Wikimedia Commons, http://commons.wikimedia.orgToday’s Agenda• Distribute homework #3•Gears– Applications– Types– Terminology / nomenclature– Congugate action – Involute curve– Analysis & designApplications of GearsSobel, Dava, LongitudeImages removed due to copyright restrictions. Please see http://mossmotors.com/Graphics/Products/Schematics/SPM-027.gifhttp://www.nmm.ac.uk/collections/displayRepro.cfm?reproID=A6263Spur 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 themGear TerminologySource: 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.Diametral pitch (teeth per inch)# of teeth on a gear with a 1 inch pitch diameter Easily confusedOther Types of GearsHelicalBevelRackWormCourtesy OSHA.Images from Wikimedia Commons, http://commons.wikimedia.orgImage courtesy of perlmonger on Flickr.Early GearsRoman watermills at Barbegal300ADApplication for powering textile machinery18thcentury Drawings of waterwheels and gears removed due to copyright restrictions.Conjugate ActionωΑABωΒLet’s say ωAis a known. How can we determine ωB?Let’s say ωAis a constant with time. Can we synthesize a shape of body B so that ωBis also constant with time?Pitch PointωΑABωΒWhat is the pitch point?What is the line of action?What are the relationships among these?Sliding and RollingωΑABωΒWhat is the relationship to the pitch circles?When one body is driving another, do the surfaces slide, roll, or both?How could you determine this?Rack Cutting• A way to get the relative motion you want• Pick one shape as you wish• Enforce the motion you want• Cut away everything that interferesGear blank rotates in this directionRack cutter reciprocates in a direction perpendicular to this pageFigure by MIT OpenCourseWare.Involute Profile• How it is constructed–Demo• Properties– Conjugate action– Allows design of whole sets of compatible gears– Conjugate action not sensitive to center distance variationsFrom Shigley and MischkeThis geometry is not an involute. More Gear TerminologyImage removed due to copyright restrictions. Please see http://commons.wikimedia.org/wiki/File:Gear_words.pngPressure Line• Where the teeth contact, the surface normal defines a pressure line• The force transmitted acts along this line• The pressure line always includes the point of tangency between the pitch circles• With the involutegear profile, the pressure line is constantFrom Shigley and MischkeBase circleBase circleAddendumcirclePressurelineThis portion of profileis not an involuteThis portion of profileis not an involuteInterference ison flank of driverduring approachCADBDriven gear 2Driving gear 1O2O1ω2ω1Figure by MIT OpenCourseWare.Gear Terminology“Line of action” & “pressure line” & “generating line”are all synonymous 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.Pressure Angle• The pressure line acts at some angle to the tangent of the pitch circles• This angle can be chosen by the designer• It affects– Separation forces– Tooth shape From Shigley and MischkeFigure by MIT OpenCourseWare.Base circleBase circleAddendumcirclePressurelineThis portion of profileis not an involuteThis portion of profileis not an involuteInterference ison flank of driverduring approachCADBDriven gear 2Driving gear 1O2O1ω2ω1Pressure angleConcept Question1. << 0.32. About 0.33. About 0.54. >> 0.5A pair of gears are mated. One is driven at a set torque, the other is regulated at a set speed. The gears are the ones circled. What is the ratio of the separation forces and the total force on the bearing? Courtesy of W. M. Berg, Inc. Used with permission.Contact Ratioaddendum of gearaddendum of pinionpitch circlearc of actionzone of actionpressure linecontact ratio = length of arc of action / pitch = average number of teeth engagedInterferenceFrom Shigley and MischkeBase circleBase circleAddendumcirclePressurelineThis portion of profileis not an involuteThis portion of profileis not an involuteInterference ison flank of driverduring approachCADBDriven gear 2Driving gear 1O2O1ω2ω1Figure by MIT OpenCourseWare.BacklashCourtesy of W. M. Berg, Inc. Used with permission.Gear Selection•Pitch• Face width• Material• Pressure angle• # of teeth• Hub style, bore, etc.Courtesy of W. M. Berg, Inc. Used with permission.• You call up the number 1-800-232-BERG and ask that, for a special application, you want a 48 pitch spur gear, but with a pitch dia of 0.32 inches. They will probably say:1. OK, no problem2. OK, but it will cost a lot3. No, this is not technically possible Courtesy of W. M. Berg, Inc. Used with permission.• You call up the number 1-800-232-BERG and ask that, for a special application, you want a 48 pitch spur gear, but with a pitch dia of half the smallest one in the catalog. They will probably say:1. OK, no problem2. OK, but it will cost a lot3. OK, but it will be weak4.