1Outline Gear Theory¾Fundamental Law of Gearing¾Involute profile 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 ==ωωpitch circle, pitch diameter d, pitch pointgearpinionWhat gear tooth shape can do this?Towards 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 Theory¾Fundamental Law of Gearing¾Involute profile Nomenclature Gear TrainsSimple Gear Trains3Simple Gear TrainRBRPPBvNNNNNNm =−−=RBRGGPPBlackBlackYYBvNNNNNNNNNNNNm −=−−−−−=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
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