Design

Prof. Samy J. Ebeid ١

Double Helical Gears

١Helical Gears

Types of Herringbone GearsHerringbone=A pattern consisting of adjoining vertical columns of slanting lines.

A helical gear having teeth that lie on the pitch cylinder in a V -shaped form so that one

half of each tooth is on a right-handed helix and the other half on a left-handed helix.

٢Helical Gears

Design

Prof. Samy J. Ebeid ٢

Static Bending Strength of Teeth

T {kgcm}=71620 x (HP/N)

T {Nm} =9550 x (KW/N)٣Helical Gears

Static Bending Strength of Teeth

٤Helical Gears

Design

Prof. Samy J. Ebeid ٣

Static Bending Strength of Teeth

kl : Lubrication factor

Gear type Lubrication grade

Helical Proper Medium Inadequate

1.15 1.25 1.35

b/m = 20 : 30 for single helical

= up to 40 for double helical

٥Helical Gears

Revision on Dynamic Loading for Spur Gears

٦Helical Gears

Design

Prof. Samy J. Ebeid ٤

A = kd . b . cos2 γγγγ + Pt

kd : Deformation factor [N/mm]

Dynamic load Static load

Linear velocity (m/s)

Av

0.151

cosAt

Pd

P+

+=γ

Dynamic Loading for Helical Gears

+=gE

1

pE1/ek

dk

E: Modulus of elasticity [N/mm2]

k: Tooth shape factor in dynamic loading

e is the probable error

k =

= 0.107 for 14.5̊ tooth

= 0.111 for 20̊ full depth tooth= 0.115 for 20̊ stub tooth

Errors in Tooth Profile:1. Probable error , which results from Manufacturing conditions.2. Permissible error, which depends on Function and is related to speed.

٧Helical Gears

Errors in Gears

٨Helical Gears

Design

Prof. Samy J. Ebeid ٥

Errors in Gears

٩Helical Gears

Revision on Endurance Strength for Spur Gears

The Endurance Strength determines the degree of safety. The endurance

strength is estimated by applying the Lewis’s formula when using σen.

We use σen to count for the stress concentration at the base of the tooth.

١٠Helical Gears

Design

Prof. Samy J. Ebeid ٦

Endurance Strength for Helical Gears

Pen > Pd

١١Helical Gears

The limiting load for wear Pw is the load beyond which

wear is likely to be rapid.

Pw > Pd

Wear Resistance

١٢Helical Gears

Design

Prof. Samy J. Ebeid ٧

١٣Helical Gears

Helical Gear Forces

١٤Helical Gears

Design

Prof. Samy J. Ebeid ٨

Example H1

A pair of helical gears are to transmit 15 kW. Theteeth are 20̊ stub in diametral plane and have a helixangle of 45̊. The pinion runs at 10 000 rpm and has80 mm pitch diameter. The gear has 320 mm pitchdiameter. If the gears are made of cast steel havingallowable static strength of 100 MPa; determine asuitable module and face width from static strength

considerations and check the gears for wear, given σ

= 618 Mpa.

١٥Helical Gears

Example H2

A helical cast steel gear with 30̊ helix angle has totransmit 35 kW at 1500 rpm. If the gear has 24 teeth,determine the necessary module, pitch diameter andface width for 20̊ full depth teeth. The static stress forcast steel may be taken as 56 MPa. The width offace may be taken as 3 times the normal pitch. Whatwould be the end thrust on the gear? The toothfactor for 20̊ full depth involute gear may be taken as0.154 – (0.192/TE), where TE represents theequivalent number of teeth.

١٦Helical Gears

Design

Prof. Samy J. Ebeid ٩

Example H3

Design a pair of helical gears for transmitting 22 kW. The speed

of the driver gear is 1800 rpm and that of the driven is 600 rpm.

The helix angle is 30 ̊ and profile is corresponding to 20̊ full

depth system. The driver gear has 24 teeth. Both gears are

made of steel with allowable static stress as 50 MPa. Assume

the face width parallel to axis as 4 times the circular pitch and

the overhang for each gear as 150 mm. The allowable shear

stress for the shaft material is 50 MPa. The form factor is 0.154

– (0.192/TE), where TE represents the equivalent number of

teeth. The velocity factor is 350/(350+v), where v is pitch line

velocity in m.min. The gears are required to be designed only

against bending failure of the teeth under dynamic condition.

١٧Helical Gears