# Helical Gear (PDF)

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```					              ENTC 463
• HW#5 Helical Gears
• Chapter 8 – 44
• Chapter 10 – 2 (change helix angle to 25
degree), 6.
ENTC 463
• Exam #1, 2/14/2008
– Chapter 7 – Belt and Chain
– Wire rope
– Chapter 8 – Spur gears and helical gear
geometry
– Chapter 9 – Spur gear design and analysis,
gear materials
– Chapter 10 – Helical gear design and analysis
Helical Gears

ENTC 463
Mechanical Design Applications II
Helical Gears
•One left hand and one right hand
• Parallel shafts

• Crossed helical gears
• Both right hand or both left hand
• Non-parallel, non-coplanar shafts
Helical Gears
– Chapter 8, geometry and material
– Chapter 10, forces and stress
– Smooth engagement
– Smaller package
– Axial thrust ?
Helical Gear Geometry

Helical angle ψ –
between the red and
blue lines
Gear Geometry
• Circular pitch
πD
p=
N
• Normal circular pitch
pn = p cosψ

• Axial pitch

p
px =
tanψ
Gear Geometry
• Diametral pitch
(transverse)
N
Pd =
D
• Normal duametral
pitch
pd
pnd =
cosψ
π             π
pd =       , pnd =        Where are they in the figure?
p             pn
Forces Acting on Helical Gear
Forces Acting on Helical Gear

Wn : normal force

Wt : tangential force

Wx : axial force
Tangential Plane (top view)
Wt : tangential force

Wx : axial force

Wx = Wt tanψ
Bottom of the cheesecake
Transverse Plane (front view)

φt : transverse pressure angle

Wr = Wt tan φt

Front shear plane of the cheesecake
Normal Plane (front view rotate ψ)

φn : normal pressure angle
used as φ

⎛ Wt      ⎞
Wr = ⎜
⎜ cosψ    ⎟ tan φn
⎟
⎝         ⎠
Wt
Geometry Parameters
Wr = Wt tan φt                      φt : transverse pressure angle
φn : normal pressure angle
⎛ Wt      ⎞
Wr = ⎜
⎜ cosψ    ⎟ tan φn
⎟                     ψ : helical angle
⎝         ⎠

Spur gear : pressure angle φ

⎛ Wt      ⎞
Wr = Wt tan φt = ⎜
⎜ cosψ    ⎟ tan φn
⎟
⎝         ⎠
tan φn                       use φn as φ
⇒ tan φt =
cosψ                         the only added parameter is ψ
True Normal Force, Wn
• True normal force Wn, can be calculated
(but not used)
Wt cosψ       Wt
Wn =         =
cos φn   cosψ cos φn

• Use other components: Wt, Wr, Wx
– Tables and Figures
– Shafts, bearings, etc.
Power - Force

D
Wt × = T
2                      ⎛ Wt     ⎞
Wr = ⎜
⎜ cosψ   ⎟ tan φn
⎟
63000 × hp              ⎝        ⎠
T=
n
126000 × hp       Wx = Wt tanψ
Wt =
nD
Helical Gear Example
• Normal diametrial pitch pnd=8, normal
pressure angle φn = 20 degree, N = 32,
F = 3.0”, ψ = 15 degree. What are the
forces acting on the gear tooth while the
gear is rotating at 650 rpm and
transmitting 7.5 hp
Stress in Helical Gears
• Bending stress number, st
–   Geometry factor J (Figure 10.5 to 7)
–   Size factor                     Use chart/Table from Chapter 9
–   Rim thickness factor
–   Dynamic factor

Wt pd
st =       Ko K s Km K B Kv
FJ
Geometry Factor, J
Assume 75 teeth meshing gear/pinion initially

4
J’=0.49

3

2

1
Geometry Factor Multiplier, K

K=1.035

N P = 30
N G = 150
J = J ′ × K = 0.49 ×1.035
Surface Stress Number
Wt K o K s K m K v
sc = C p
FDP I

• Geometry factor, I
Bending Stress Consideration
Wt pd                                         Wt pd
Stress:   σt =           Bending stress number:         st =
FJ                                            FJ
Wt pd
Modified bending stress number:    st =       Ko K s Km K B Kv
FJ

Compare
Allowable bending stress (strength):   sat
′           YN
Adjusted allowable bending stress (strength):   sat       = sat
SF ⋅ K R
Contact Stress Consideration
Wt
Contact stress number:     σc = Cp
FDP I

Wt K o K s K m K v
Modified contact stress number:     sc = C p
FDP I

Compare
Allowable contact stress (strength):   sac
′          Z N CH
Adjusted allowable contact stress (strength):     sac       = sac
SF ⋅ K R

```
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