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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 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
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