Worm and Worm Gear

ENTC 463Mechanical Design Applications II

ENTC 463

• Lab. #2 Gears• To be scheduled• Thompson 009B

ENTC 463

• HW#7 Worm and Wormgear• Due 2/28/2008• Chapter 8 – 55• Chapter 10 – 19

Worm Gear Drive

Figure 14.4 Worm gear drive. (a) Cylindrical teeth; (b) double enveloping.

Hamrock Text Reference: Figure 14.4, page 618

Worm and Worm Gear

Non-parallel, non-coplanar shafts

Worm and Worm Gear

• Worm– Rotate at high speed, with thread similar to screw– Similar to a special form of a gear introduced– Axial pitch: the distance from a point on the thread to

corresponding point on the next thread• Worm Gear

– Similar to spur gear• Form worm and worm gear to mesh

– Axial pitch of worm = circular pitch of wormgear

xG

G pNDp ==π

Worm Geometry

• Number of worm threads (starts), Nw– Nw =1, similar to a 1-tooth helical gear with

large helix angle wraps around the face• Lead, L

– Axial distance that a point would move at one revolution

Worm and Worm Gear Geometry

• Lead angle, λ

• Pitch line speed, vt (ft/min)

( ) xWw pNLDL ×== − ,tan 1 πλ

12

12GG

tG

WWtW

nDv

nDv

π

π

=

= Pitch line speed of the worm is not equal to the pitch line speed of the wormgear

Sliding

Next Thursday2/28/2008

Meet @ Thompson 009B

ENTC 463Mechanical Design Applications II

Higginbotham to Winniford– 2:20 to 3:00 PMAllen to Hagan – 3:00 to 3:35 PM

Worm and Worm Gear Geometry

• Pressure angle (similar to helical gear)

• Example

λφφ costantan tn =

in 2,rpm 1750,3,6 ==== WWWd DnNp

?,,,,,, tGx vCDLpp λ

Typical dimension

• Diameter of worm

• Tooth geometry5.2

875.0CDW =

Typical Dimension

• Face width of wormgear

• Face width (length) of wormd

G pF 6

=

diameterThroat :

222

21

22

t

Gtw

D

aDDF

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−−⎟

⎠⎞

⎜⎝⎛=

Forces Acting on Worm and Worm Gear

Worm

Worm gear

tWxG

rGrW

WWWW

==

rGrW

tGxW

WWWW

==

Forces Acting on Worm and Worm Gear

friction oft coefficien :sincoscos

sinsincoscoscossincos

2

μλμλφ

φλμλφλμλφ

−=

−+

=

=

n

ntGrG

n

ntGxG

G

otG

WW

WW

DTW

Sliding

• Sliding between worm and worm gear – Different from other types of gears– Sliding friction (not rolling friction)– Sliding velocity can be calculated

λλ cossintWtG

svvv ==

Estimate Coefficient of Friction

Friction Force and Friction Power Loss

ft/min)in (

33000

sin))(cos(cos

s

fsL

n

tGf

v

WvP

WW

=

−=

λμφλμFriction force:

Friction power loss:

Input and output power: Loi PPP +=

Efficiency:i

o

PP

=η

Factors Affecting Efficiency

↑↑

−=

f

n

tGf

W

WW

,

sin))(cos(cos

μ

λμφλμ

70%) to(60 efficiency low,5 :locking self o<λ

Worm Gear Stress Analysis

• Only worm gear is analyzed since threads are more durable and made from a stronger material

• Different from other types of gears• Bending stress analysis• Surface durability

Bending Stress

n

d

yFpW

=σ

pitchcircular normal : widthface :

factor form Lewis :gear teethon load dynamic :

n

d

pFyW

dn p

pp λπλ coscos ==

12

12001200

GGtG

tGv

v

tGd

nDv

vK

KWW

π=

+=

=

Material Selection Based on Bending Stress

material ofstrength fatigue vs.n

d

yFpW

=σ

Fatigue strength of material: 0.35 times the ultimate strengthFor manganese gear bronze: 17000 psiFor phosphor gear bronze: 24000 psi

Surface Durability

vmeGstR CCFDCW 8.0

:load tangental)(allowableRated

=

factor velocity :factor correction ratio :

)67.0,min( width,face effective : wormgear theofdiameter pitch :

)properties (materialfactor material :

v

m

Wee

G

s

CC

DFFFDC

=

Material Factor

Ratio Correction Factor

Velocity Factor

Examples

• Design worm and worm gear based on:

rpm 1750in 0.2in 67.8

2014.04

lb.in 4168

====

=

=

W

W

G

n

o

nDD

T

o

o

φ

λ