Involute Gear Tooth Bending Stress Analysis

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1 Involue Gear Tooh Bending Sress Analysis Lecure 21 Engineering 473 Machine Design

2 Gear Ineracion Line of Ceners Line Tangen o s Line Normal o Line of Ceners

3 1 s Close Up of Meshed Teeh Line of Conac W H W H Line Tangen o s

4 2 nd Close Up of Meshed Teeh Line of Conac W H W H

5 3 rd Close Up of Meshed Teeh Line of Conac

6 Line of Acion/Pressure Angle Line of Acion Line angen o boh base circles Pressure Angle Angle beween he line normal o he line of ceners and he line of acion. Pich Poin Inersecion of he line of ceners wih he line of acion Line of Conac Pich Poin Line of Acion W H W H φ Pressure Angle Line of Ceners

7 Pich Circle Pich Circle Circle wih origin a he gear cener and passing hrough he pich poin. Pich Circle φ Pich Circle

8 Relaionship Beween Pich r rcos( φ) b and s Pich Circle φ Pich Circle r b r

9 Torque Relaionship T Power Angular Velociy P ω T P(hp) n (rev/min) 550 lb f sec 1.0 hp 1.0 rev 2π rad 60 sec min 12 in f T 63,000 P n ( lb in)

10 Tooh Load Equaions W T d/2 W r H W anφ W W cosφ Line of Acion Line of Conac W H W r W H W φ Pressure Angle Line of Ceners

11 Gear Tooh Failure Mechanisms The primary failure mechanisms for involue gear eeh are: 1) excessive bending sresses a he base of he ooh and, 2) excessive bearing or conac sress a he poin of conac. Deuschman, Fig Mo, Fig The American Gear Manufacurers Associaion (AGMA) has developed sandard mehods for addressing boh failure mechanisms.

12 AGMA Publicaions Sandand , Nomenclaure of Gear Tooh Failure Modes, AGMA, Alexandria, VA, Sandard 6010-E88, Sandard for Spur, Helical, Herringbone, and Bevel Enclosed Drives, AGMA, Alexandria, VA, Sandard 2001-C95, Fundamenal Raing Facors and Calculaion Mehods for Involue Spur and Helical Gear Teeh, AGMA, Alexandria, VA, Sandard 908-B89, Geomery Facors for Deermining he Piing Resisance and Bending Srengh of Spur, Helical and Herringbone Gear Teeh, AGMA, Alexandria, VA 1989.

13 Lewis Equaion σ M I c M W L I c 1 12 b 3 2 b 6 2 σ 6WL 2 b Deuschman, Fig

14 Lewis Equaion Lewis Equaion (Coninued) (Coninued) 4L x 2 L x L 1 b W 6L 1 b W σ b 6W L σ

15 Lewis Equaion Lewis Equaion (Coninued) (Coninued) bpy W σ 3p 2x y p p x 1 b W σ 4L x L 1 b W σ 2 2 Lewis Form Facor p circular pich

16 Lewis Equaion (Coninued) y 2x 3p σ W bpy Y can be deermined graphically or by a compuer. P Y σ Diameral Pich πy WP by π p Mos commonly used form of Lewis Equaion

17 Lewis Form Facor (Example Values) Values are for a normal pressure angle of 20 degrees, full-deph eeh, and a diameral pich of one. σ WP by Shigley, Table 14-2

18 Limiaions of he Lewis Equaion 1. Assumes ha maximum bending load occurs a he ip. Maximum load occurs near he pich circle when one ooh carries all of he orque induced load. 2. Considers only bending componen of he force acing on he ooh. The radial force will cause a compressive sress over he base cross secion. 3. Doesn consider conac sresses. 4. Assumes ha he loads are saic. The AGMA has developed a number of facors o be used wih he Lewis Equaion ha will lead o an accepable design.

19 σ WP FJ d The AGMA Equaions K a K s K m K v σ all S K a T K K L R F face widh (b) K K K K J Geomery facor P d a s v d Pich Diameer N Number of Teeh W m Applicaion facor Size facor Load disribuion facor Dynamic facor Diameral Pich N d Tangenial Load S K K K a L T R AGMA Allowable Sress Number Life facor Temperaure Facor Reliabiliy Facor Facors are used o adjus he sress compued by he Lewis equaion. Facors are also used o adjus he srengh due o various environmenal condiions. Shigley conains ables and chars for many of hese facors.

20 AGMA Form Facor Noe ha he AGMA Form Facor will resul in a lower sress han he Lewis Equaion. Mo, Fig. 19-5

21 AGMA Allowable Bending Sress Numbers Grade 1 is he basic or sandard maerial classificaion. Grade 2 requires beer han normal microsrucure conrol. Mo, Fig. 9-8

22 AGMA Dynamic Facor The AGMA Dynamic Facor is used o correc he bending sress number for dynamic effecs associaed wih: 1. Inaccuracies in ooh profile, ooh spacing, profile lead, and run-ou, 2. Vibraion of he ooh during meshing due o ooh siffness; 3. Magniude of he pich-line velociy, 4. Dynamic unbalance of he roaing members, 5. Wear and permanen deformaion of conacing surfaces, 6. Shaf misalignmen and deflecion, and 7. Tooh fricion.

23 Dynamic Facor Char Q v AGMA Qualiy Number The AGMA sandards conain olerances for each qualiy number. Pich Line Velociy rω The dynamic facor in Shigley is equal o he reciprocal of he dynamic facor given in his char. Mo, Fig. 9-19

24 Assignmen 1. A spur pinion has a pich of 6 eeh/in, 22 full-deph eeh, and a 20 degree pressure angle. This pinion runs a a speed of 1200 rev/min and ransmis 15 hp o a 60-ooh gear. If he face widh is 2 in, esimae he bending sress. 2. A seel spur pinion has a module of 1.25 mm, 18 full deph eeh, a pressure angle of 20 degrees, and a face widh of 12 mm. A a speed of 1800 rev/min, his pinion is expeced o carry a seady load of 0.5 kw. Deermine he resuling bending sress.

Chapter = For one gear straddle-mounted, the load-distribution factor is:

Chapter = For one gear straddle-mounted, the load-distribution factor is: Chaper 15 15-1 iven: Uncrowned, hrough-hardened 300 Brinell core and case, rade 1, N C 10 9 rev of pinion a R 0.999, N 0 eeh, N 60 eeh, Qv 6, d 6 eeh/in, normal pressure angle 0, shaf angle 90, n p 900

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