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-- 2010-06-09

-helical gear geometry parameters and calculated -

For the spiral bevel gear's tooth shape, the axis perpendicular to the gear face (subscript in t that) and perpendicular to the tooth profile of the French helicoid surface (subscript to n that) have different parameters. The end is a standard helical gear involute, helical gear from the processing and mechanical point of view, helical gear of the law should be the standard surface parameter values.

1. Helix angle β

Shown on the right for the helical gear indexing cylinder expansion plan, launched into a straight line spiral, the angle β with the axis line is called helical gear on the dividing cylinder helix angle, referred to as helical gear spiral angle.

tanβ = πd / ps

For the same reason, obtaining the base cylinder helix angle βb as:

So are:

... (9-9-01)

Usually sub-degree circle on the β helix angle oblique to the calculation of the geometric dimensions. Larger spiral angle β, the more inclined teeth, the better transmission of stationarity, but the greater the axial force. Usually taken in the design. For the Son of Man gear, the axial force can be offset, often taken, but the process more difficult, usually for heavy machinery gear drive.

Involute gear tooth profile according to the rotation of spiral surface can be divided into two kinds of D-and L-. How to determine what about spin? Test?

2. Modulus

As shown, pt pitch for the face, but for the law face pitch pn, pn = pt · cosβ, because p = πm, πmn = πmt · cosβ, so helical gear and the end-plane modulus modulus relationship : mn = mt . cosβ.

3. Pressure angle

Due to oblique helical gears and gear rack, they face pressure from the French pressure angle and face angle should be equal, respectively, the helical gear pressure angle normal surface pressure angle αt αn and end the relationship can be inclined rack. Shown on the right of the ramp in the rack, the plane ABD in the side surface, flat surface S on the ACE in the law, ∠ ACB = 90 °. In the right angle △ ABD, △ ACEJ and △ ABC in,,,, BD = CE, so there:

... (9-9-03)

>> Law of the pressure surface pressure angle and face angle of the relationship between <<

4. Addendum Coefficient and headspace factor:

Either from normal or from the end point of view, the high top gear tooth are the same, the top gap is the same, namely,

5. Helical gear geometry calculation: as long as the spur gear geometry of the various parameters of the calculation formula as the end parameter is entirely applicable to the standard parallel shaft helical gear geometry calculation, the specific formula in the following table :

Name

Symbol

Company Type

Pitch circle diameter

d

d = mz = (mn / cosβ) z

Base circle diameter

db

db = dcosαt

Tooth crown heights

ha

ha = h * anmn

High tooth

hf

hf = (h * an + c * n) mn

The whole tooth

h

h = ha + hf (2h * an + c * n) mn

Addendum circle diameter

da

da = d +2 ha

Center distance

, A

a = (d1 + d2) / 2 = mn (z1 + z2) / 2cosβ

As can be seen from the table, the center of helical gears and spiral angle β away from the. When a pair of helical gear module, teeth fixed, by changing the helix angle β way to Minato distribution center distance.

For the spiral bevel gear's tooth shape, the axis perpendicular to the gear face (subscript in t that) and perpendicular to the tooth profile of the French helicoid surface (subscript to n that) have different parameters. The end is a standard helical gear involute, helical gear from the processing and mechanical point of view, helical gear of the law should be the standard surface parameter values.

1. Helix angle β

Shown on the right for the helical gear indexing cylinder expansion plan, launched into a straight line spiral, the angle β with the axis line is called helical gear on the dividing cylinder helix angle, referred to as helical gear spiral angle.

tanβ = πd / ps

For the same reason, obtaining the base cylinder helix angle βb as:

So are:

... (9-9-01)

Usually sub-degree circle on the β helix angle oblique to the calculation of the geometric dimensions. Larger spiral angle β, the more inclined teeth, the better transmission of stationarity, but the greater the axial force. Usually taken in the design. For the Son of Man gear, the axial force can be offset, often taken, but the process more difficult, usually for heavy machinery gear drive.

Involute gear tooth profile according to the rotation of spiral surface can be divided into two kinds of D-and L-. How to determine what about spin? Test?

2. Modulus

As shown, pt pitch for the face, but for the law face pitch pn, pn = pt · cosβ, because p = πm, πmn = πmt · cosβ, so helical gear and the end-plane modulus modulus relationship : mn = mt . cosβ.

3. Pressure angle

Due to oblique helical gears and gear rack, they face pressure from the French pressure angle and face angle should be equal, respectively, the helical gear pressure angle normal surface pressure angle αt αn and end the relationship can be inclined rack. Shown on the right of the ramp in the rack, the plane ABD in the side surface, flat surface S on the ACE in the law, ∠ ACB = 90 °. In the right angle △ ABD, △ ACEJ and △ ABC in,,,, BD = CE, so there:

... (9-9-03)

>> Law of the pressure surface pressure angle and face angle of the relationship between <<

4. Addendum Coefficient and headspace factor:

Either from normal or from the end point of view, the high top gear tooth are the same, the top gap is the same, namely,

5. Helical gear geometry calculation: as long as the spur gear geometry of the various parameters of the calculation formula as the end parameter is entirely applicable to the standard parallel shaft helical gear geometry calculation, the specific formula in the following table :

Name

Symbol

Company Type

Pitch circle diameter

d

d = mz = (mn / cosβ) z

Base circle diameter

db

db = dcosαt

Tooth crown heights

ha

ha = h * anmn

High tooth

hf

hf = (h * an + c * n) mn

The whole tooth

h

h = ha + hf (2h * an + c * n) mn

Addendum circle diameter

da

da = d +2 ha

Center distance

, A

a = (d1 + d2) / 2 = mn (z1 + z2) / 2cosβ

As can be seen from the table, the center of helical gears and spiral angle β away from the. When a pair of helical gear module, teeth fixed, by changing the helix angle β way to Minato distribution center distance.

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