Worm gearing . be considered, and it is the effect of the relative motion betweenthe worm and wheel. Thus with a approaching zero valuethe relative motion between the two is very high compared tothe useful motion of the worm wheel; hence much work isdissipated in useless friction. Various formulae have been proposed for determining theactual mechanical efficiency of worm gears, and so far aspossible, these will be examined next. We will take first, the much quoted formula developed byProfessor Barr of Glasgow University: V = tan a (1 —/jl tan a)tan oc-\r2/jL (76) 72 WORM GEARS For various angl
Worm gearing . be considered, and it is the effect of the relative motion betweenthe worm and wheel. Thus with a approaching zero valuethe relative motion between the two is very high compared tothe useful motion of the worm wheel; hence much work isdissipated in useless friction. Various formulae have been proposed for determining theactual mechanical efficiency of worm gears, and so far aspossible, these will be examined next. We will take first, the much quoted formula developed byProfessor Barr of Glasgow University: V = tan a (1 —/jl tan a)tan oc-\r2/jL (76) 72 WORM GEARS For various angles of thread, a, the efficiencies have beenplotted in column II table IX. Next, Professor Unwin (Elements of Machine Design, Vol. 1,p. 423) gives the following: 1 -u cot a (77) Column III of the table gives these values. Francis W. Davis, , has proposed the following: , = !-.( ^ r-) («) Comparing this equation with (77), it will be noted thatUnwins may be written. //(cot a + tan a) (79) l+jj. tan a (80) COS a sm a + n sm o:^ very closely resembling (78). The values of /j. in this equationare given in Column IV. It must be observed here that neither of the above formulaetakes into account the pressure angle, and this undoubtedlyexercises a considerable influence upon the efficiency of thegear inasmuch as it very largely governs the normal toothpressure, quite irrespective of the torque. See equation 43,Chapter VII. The force of friction in the gears is equal to fiXp^, and thisforce tends to resist the gliding of the worm over the wheeltooth. It is evident that the path along which the gildingoccurs is a helical line wound around a cylinder whose diameterequals the pitch diameter of the worm, and the length of thispath is I, the length of thread per revolution measured at thepitch line. See equation 15, Chapter IV. The work lost infriction equals in foot pounds 12 ^^^) EFFICIENCY OF WORM GEARING 73 The work put into the worm is Tndp12Hence, the e
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