TAILIEUCHUNG - Gears P2

When the center distance is increased by a relatively small amount, ∆C, a backlash space develops between mating teeth, as in Figure . The relationship between center distance increase and linear backlash, BLA, along the line of action, is: BLA | L inryjr R Angulo Ql - Bifl 2 B t When the center distance is increased by a relatively small amount AC a backlash space develops between mating teeth as in Figure . The relationship between center distance increase and linear backlash Bla along the line of action is Bla 2 AC sin 21 This measure along the line-of-action is useful when inserting a feeler gage between teeth to measure backlash. The equivalent linear backlash measured along the pitch circle is given by B 2 AC tan 0 22a where AC change in center distance pressure angle Hence an approximate relationship between center distance change and change in backlash is AC Ab for 14 pressure-angle gears AC Ab for 20 pressure-angle gears 22b 22c T47 Although these are approximate relationships they are adequate for most uses. Their derivation limitations and correction factors are detailed in Reference 5. Note that backlash due to center distance opening is dependent upon the tangent function of the pressure angle. Thus 20 gears have 41 more backlash than 14 gears and this constitutes one of the few advantages of the lower pressure angle. Equations 22 are a useful relationship particularly for converting to angular backlash. Also for fine-pitch gears the use of feeler gages for measurement is impractical whereas an indicator at the pitch line gives a direct measure. The two linear backlashes are related by Bla 23 B --------- cos 0 The angular backlash at the gear shaft is usually the critical factor in the gear application. As seen from Figure this is related to the gear s pitch radius as follows B 24 aB 3440 ------ arc minutes R1 Obviously angular backlash is inversely proportional to gear radius. Also since the two meshing gears are usually of different pitch diameters the linear backlash of the measure converts to different angular values for each gear. Thus an angular backlash must be specified with reference to a particular shaft or gear center. Summary of Gear Mesh Fundamentals The

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