Gear Ⅰ Spur Gears R&D Cener
www.kepial.com 1. Sanar of gear (KS) (1) erms of gear. KS B 0102 (2) Sanar of expression an geomerical aa of gear KS B 0053 (3) echnical rawings Represenaions of gears KS B 0002 2. erms of gear [Figure 1] erms of gear Clearance [Figure 2] Clearance 2
www.kepial.com [Figure 3] erms of gear eeh (1) Pich poin : a poin where he line of acion mees he line rawn beween cener of wo gears, he poin where pich circles of wo gears mee (2) Pich circle : a circle rawn hrough he pich poin from each gear cener (3) Base circle : a base circle where an involue curve is rawn (4) Line of acion : a common angen line rawn a he plane of conac of he ooh plane when inermeshing gears roae; i represens he irecion of acion of he forces. (5) Pressure angle : an angle beween he line of acion an he common angen line of pich circle of engaging wo gears (6) Aenum circle : a circle rawn by connecing he op of gear eeh (7) Deenum circle : a circle rawn by connecing he roo of gear eeh (8) Aenum : isance beween pich circle an aenum circle (9) Deenum : isance beween pich circle an eenum circle (10) Circular pich : an arc of a circle of a ooh a circumference of pich circle, a circumference of pich circle ivie by ooh number, sum of an arc of a circle of pich circle of ooh an ooh groove. (11) Normal pich : same value wih base circle pich, he isance beween a ooh an an ajacen ooh on common angen line (12) Clearance : isance from a cener of one aenum circle of a gear o a cener of a eenum circle of an opposing gear (13) Whole eph : oal heigh of ooh = aenum + eenum (14) Working eph : sum of aenum of a pair of gears 3
www.kepial.com (14) Backlash : a gap beween ooh surface (Backlash on he circular pich, backlash irecion o he angen line, backlash irecion o he raius) 3. Basic heory of gear 31. ooh profile of gear (1) Coniion of engagemen of gears : When wo gears engage, hey shoul be in conac a a poin on he ooh profile curve. o preven separaion or igging of ooh profiles, wo gears shoul have he same velociy of a angen line irecion a conac Q. [Figure 4] ooh profile curve (2) heory of mechanics coniion of ooh profile curve * O 1, O 2 Roaional cener, fixe poin * he rae of gear velociy : Consan Velociy a he Q poin of gear 1 v1 1 r 1 Velociy a he Q poin of gear 2 v2 2 r 2 4
www.kepial.com Velociy of a angen line irecion = v1 cos 1 v2 cos 2 r cos r cos 1 1 1 2 2 2 1 r2 cos 2 O2 N2 O2P r cos O N O P 2 1 1 1 1 1 O N P O N P Similar figures 1 1 2 2 1 * P poin : he poin which ivies cener isance OO 1 2 inernally ( ) fixe poin pich poin 2 32. Pich poin (1) Camus heorem : In a conac poin, a common angen line buil a he ooh profile passes he pich poin. 1 here are a lo of curves which saisfy he coniion. 2 We limi he number o 2 or 3 curves in he pracical view. 3 Involue curve an Cycloi [Figure 5] Principle of he Involue ooh profile 5
www.kepial.com 33. Backlash [Figure 6] Backlash (1) wo mehos o make a backlash 1 A meho in which oal ooh hickness a he circular pich is as shor as a backlash of circumference of circular pich : We can ivie he backlash lengh of gear engagemen in half or we can eermine he ooh hickness of he gear(rive shaf) p/2 an he ooh hickness of he gear(engaging) p/2f. 2 A meho in which cener isance is as long as f r 34. Cycloi ooh profile (1) A rajecory of a poin on he rolling circle when a small rolling circle rolls on he base circle wihou sliing. (2) Cycloi curve 1 Epicyclois curve : A curve rawn ousie of he pich circle 2 Hypocycloi curve : A curve rawn insie of he pich circle 6
www.kepial.com [Figure 7] Cycloi ooh profile curve 35. Involue ooh profile [Figure 8] Involue ooh profile curve 7
www.kepial.com (1) FF 1 is he raius of curvaure of involue curve. (2) Base circle Involue ooh profile curve exiss only ousie of he base circle 36. Involue ooh profile an Cycloi ooh profile [able 1] Involue ooh profile an Cycloi ooh profile Involue ooh profile Cycloi ooh profile Pressure angle Consan Changing Specific sliing/abrasion Cuing ool Design meho Cener isance/ Assemble Specific sliing changes a he ooh surface an he ooh profile is collapses easily a he ooh op an he pich circle. Specific sliing is 0 a he pich poin. / Unbalance abrasion, change of he ooh profile A sraigh line(rapezium). I is easy o esign an he price is reasonable. A few errors are accepable ue o space. A possible profileshife cuing. he gears engage in heory of mechanism in spie of a few errors of cener isance of he gear box / Easy Unercu O X Compaibiliy Applicaion Inermeshing A pressure angle an moule shoul be he same. Moors, general applicaions Applie pressure is high because of inermeshing beween relief planes. Specific sliing is same a all ooh surfaces an he ooh profile wears own uniformly. Uniform specific sliing is he bes hing abou cycloi gears. A cycloi curve. Cuer varies wih rolling circle. An accurae size is require. An impossible profileshife cuing. An accurae size is require or he gears won engage in mechanism heory. here is possibiliy of ooh profile amage. / Difficul. A circular pich an rolling circle shoul be he same. Precision insrumens(waches, insrumens) Applie sress is lower han an involue ooh profile because of inermeshing beween he relief plane an inaglio plane. 8
www.kepial.com 37. Engagemen of Involue ooh profile [Figure 9] Properies of an Involue ooh profile (1) Properies of Involue ooh profile curve r b1 : Raius of a base circle Search for a plae ha conacs wih an Involue ooh profile (plae goes up an own) h C C r Velociy v 1 2 b1 Differeniae by ime h v rb 1 rb 1 * Gear roaes a a consan velociy A slab is life a a consan velociy Uniform moion 9
www.kepial.com [Figure 10] Properies of an Involue ooh profile r C C r b1 1 1 2 b2 2 r r r r 1 2 b1 b2 b1 1 b2 2 r CO r CO 1 b2 2 2 b1 1 he raius of he base circle of every gear is eermine. Gears can roae a a consan spee alhough he cener isance of a pair of Involue gears changes. However, he inermeshing pich circle an pressure angle also change. 10
38. Normal pich (1) he isance beween an Involue line group on a base circle mainains P n (Normal pich) www.kepial.com [Figure 11] Normal pich [Figure 12] Pich an cener isance by base circle an pich circle 11
Raius of base circle r, iameer b b 2 rb Circumference of base circle pn Z ooh number Z Raius of pich circle r r rcos, cos b b Circular pich p Z b cos Normal pich pn pcos Z Z 1 2 b 1 b2 Cener isance A 2 2cos * Sanars of gear proucion : ooh number Pressure angle Moule * Make he same value of moule an pressure angle of wo engaging gears. b www.kepial.com 39. Size jugemen of gear ooh (1) Alhough he size of he pich circle is he same, we can a or remove gear eeh. As such, we nee a sanar size of gear ooh. (2) hree sanars regaring he size of gear eeh 1 Circular pich : p [Figure 13] Size jugemen of gear ooh(juge by circular pich) D P Z * he resul has a ecimal poin because of As such, i is ifficul o calculae. 12
www.kepial.com 2 Moule : m (=aenum) [Figure 14] Size jugemen of gear ooh(juge by moule) Moule D m P Z 3 Diameral pich : [Figure 15] Sie jugemen of gear ooh(juge by iameer pich) Z P D[inch] 13
310. Normal value of moule www.kepial.com (1) If we eermine moule an iameer pich as we please, i is inconvenien o esign a gear because of a lo of sizes an ypes of ooh. As such, he normal value of a moule an iameer pich is eermine. (ISO, DIN, KS, ec.) [Figure 16] Various moule size 311. Involue funcion [Figure 17] Involue ooh profile 14
www.kepial.com Q Q 1 r an r ( ) b b an inv [ ra ] * A correlaion of a sraigh line beween a poin a any involue funcion an a cener of a base circle an of a saring poin of an Involue an a conac poin as of a sraigh line. 312. ooh hickness calculaion a any raius [Figure 18] ooh hickness calculaion a any raius [Figure 19] ooh hickness 15
www.kepial.com *,, r correlaions ( r b : raius of base circle, : base pressure angle) 2 r,, 2r r 2 2r 2r 2r In he figure: inv inv 2r 2r Arrange he equaion by * 2 r ( inv inv ) ( inv inv ) 2r We calculae an We can calculae using he equaion r r cos r cos a any raius r. b * Wha is R when inv inv 0 is 0? inv inv calculaion 2r rb r cos r calculaion I is normally easy o calculae a any raius r. Bu if we wan o know r when is 0, we nee a mahemaic echnique. 313. Sanar Spur Gear Correlaion ooh number p p Moule m ( z ) Pressure angle z Clearance c 0.25m Aenum ha m Deenum h m c 1.25m f [able 2] Spur gear correlaion Sanar Spur gear correlaion 16
Whole eph h h h 2.25m Working eph h h c 2m Calculaion iem Diameer of pich circle Diameer of aenum circle Diameer of eenum circle w p a mz f 2 h ( z 2) m a p a 2 h ( z 2) m 2c f p f Diameer of base circle b pcos mz cos Circular pich p m b Normal pich pn p cos mcos z Arc ooh hickness p m p (on pich circle) 2 2 Arc ooh hickness (on base circle) Arc ooh hickness on any cirlcle Limi of sharpness of he ege Displacemen over a given number of eeh Displacemen over a given number of eeh (profileshife gear) Displacemen over a given number of eeh (profileshife gear +backlash) Overpin measuremen (even ooh) Overpin measuremen (o ooh) p ( inv ) b b p ( zinv ) mcos 2 inv b 0( b 0 a base circle) p ( inv inv ) p p 0 inv inv p mcos [ ( z 0.5) zinv ] m m mcos [ ( z 0.5) zinv ] 2xmsin m m www.kepial.com mcos [ ( z 0.5) zinv ] 2xmsin cos cos m m m m mz cos cos mz cos 90 cos( ) cos z p p 17
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