1Outline Gear Theory Nomenclature Gear TrainsFundamental Law of GearingFunctionally, a gearset is a device to exchange torque for velocityP=Tωthe angular velocity ratio of the gears of a gearset must remain constant throughout the meshinoutinoutVrrm ==ωωTowards the Involute ProfileA belt connecting the two cylindersline of action, pressure angle φThe Involute ProfileMeshingpressure angle, line of action, length of action, addendumNomenclatureFigure 11-8Ndpcπ=2Pitches, Etc.circular pitch (mm, in.)base pitch (mm, in.)diametral pitch (teeth/in.)module (mm/teeth)Ndpcπ=φcoscbpp =dNpd=Ndm =Velocity Ratiopitches must be equal for mating gears, thereforeinoutinoutVNNrrm ±=±=Contact Ratioaverage number of teeth in contact at any one time =length of action divided by the base pitch, or, φπcosZpmdp=()()()()φφφsincoscos2222CrarrarZgggppp−−++−+=where C=center distance=(Ng+Np)*1/pd*1/2Minimum # of Teethminimum # of teeth to avoid undercutting with gear and rackφ2minsin2=NOutline Gear Theory Nomenclature Gear TrainsSimple Gear Trains3Simple Gear TrainRBRPPBvNNNNNNm =⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−=Velocity RatioRBRGGPPBlackBlackYYBvNNNNNNNNNNNNm −=⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛−=Simple Gear Train Fine for transmitting torque between ¾shafts in close proximity¾when mvdoes not need to be too large Use third gear (“idler”) only for directional reasons (not for gear reduction)Reverse on a CarActual Manual Transmission For More Online AGMA How Stuff Works
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