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WORM GEAR DESIGN CALCULATION PDF

admin  | 15-09-2021
[RAND-1-100] Comments

A worm gear box must contain a worm and a mating gear (helical gear) and
normally the axis of the worm is perpendicular to the axis of the gear. Look at
the picture below:

Formulas for gear calculation. To design a gear tooth profile which rolls
through the mesh without friction. Formulas for gear calculation - external
gears. Download Free Lecture Notes-Pdf Link-IX. A box must contain a worm and a
mating gear (helical gear) and normally the axis of the worm is perpendicular to
the axis of the gear. Worm and WormGear Design Equations and Calculator. Gears
Engineering and Design. Equations for American Standard Fine Pitch Worms and
Wormgears Per. P = Circular pitch of wormgear P = axial pitch of the worm P x, =
in the central plane P x = Axial pitch of worm P n = Normal circular pitch of
worm and wormgear = Px cos λ = P cos ψ.

Where,

Calculations for worm gears are the same as for. Worm Gearing 50 Lead Angle Worm
threads are. Perature and the details of the gear mesh design. Worm gear.pdf -
Free download as PDF File (.pdf), Text File (.txt) or read. Of a worm gear is
related to its circular pitch and number of teeth Z by the formula.

D1 – Pitch Diameter of Worm

D2 – Pitch Diameter of Gear


WORM GEAR RATIO FORMULA

C – Centre to Centre Distance between the Worm and the Gear

This worm gear design tutorial will discuss up to the selection of the module
and pitch and the calculation of the number of teeth, pitch circle diameter and
centre to centre distance between the worm and gear. We will use the AGMA
formulae for doing the calculations. Design calculations of the other aspects of
the worm gear will be discussed in a subsequent part of the tutorial.


STEPS OF THE DESIGN CALCULATION

 * The axial pitch of the worm and the circular pitch of the gear must be same
   for a mating worm and gear. We will use the term Pitch (P) for both the pitch
   in this tutorial.
 * Also, the module of the worm as well as the gear must be equal for a mating
   worm and gear.
 * Now, let’s say we have the following design input:

Speed of the Worm (N1) = 20 RPM

Speed of the Gear (N2) = 4 RPM

 * And, we have to find out the Module (m), Pitch (P), Number of helix of Worm
   (T1), Number of teeth of Gear (T2), Pitch circle diameter of Worm (D1), Pitch
   circle diameter of Gear (D2), Centre to centre distance(C).

 * Select the suitable module and its corresponding pitch from the following
   AGMA specified table:

Module m (in MM) – Pitch P (in MM)

2 ————————-6.238


WORM GEAR CALCULATION

2.5 ———————- 7.854

3.15 ——————— 9.896

4 ————————- 12.566

5 ————————- 15.708

6.3 ———————– 19.792

8 ————————– 25.133

10 ————————- 31.416

12.5 ———————– 39.27

16 ————————– 50.625

20 ————————– 62.832

 * Say, we are going ahead with the Module as 2 and the Pitch as 6.238.

 * Use the following gear design equation:

N1/N2 = T2/T1

And, we will get:

T2 = 5 * T1……………….Eqn.1

 * Now use the following AGMA empirical formula:

T1 + T2 > 40………………Eqn.2

 * By using the two equations (Eqn.1 & Eqn.2), we will get the approximate
   values of

T1 = 7 andT2 = 35

 * Calculate the pitch circle diameter of the worm (D1) by using the below AGMA
   empirical formula:

D1 = 2.4 P + 1.1

= 16.0712 mm

 * The following AGMA empirical formula to be used for calculating the pitch
   circle diameter of the gear (D2):

D2 = T2*P/3.14

= 69.53185 mm

 * Now, we can calculate the centre to centre distance (C) by the following
   equation:

C = (D1 + D2)/2

= 42.80152 mm

 * The below empirical formula is the cross check for the correctness of the
   whole design calculation:

(C^0.875)/2 <= D1 <= (C^0.875)/1.07

Observe that our D1 value is falling in the range.


CONCLUSION

The worm gear box design calculation explained here uses the AGMA empirical
formulas. A few worm gear design calculator are available on web, and some of
them are free as well.

In the next worm gear box design calculation tutorial we will discuss the force
analysis of a worm gear box.


RELATED READING

Helical Gear vs. Spur Gear: If you have observed a spur gear application, you
may have noticed that spur gear can be replaced by helical gear. Where should a
helical gear should be used? What are the benefits and disadvantages of doing
so?

Input Parameters

Teeth type - common or spiral

Gear ratio and tooth numbers

Pressure angle (the angle of tool profile) α

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Module m (With ANSI - English units, enter tooth pitch p = π m)

Unit addendum ha*

Unit clearance c*

Unit dedendum fillet rf*

Face widths b1, b2

Unit worm gear correction x

Worm size can be specified using the:

 * worm diameter factor q
 * helix direction γ
 * pitch diameter d1

Auxiliary Geometric Calculations



Calculated parameters

Common gearing ZN

Axial module

mn = m

Normal module

mx = mn cos γ

Axial pressure angle

αx = a

Normal pressure angle

αn = arctg (tg α cos γ)

Helix/lead angle

γ = arcsin z1/q

Spiral gearing ZA

Axial module

mn = mx / cos γ

Normal module

mx = m

Axial pressure angle

αn = arctg (tg α cos γ)

Normal pressure angle

αx = α

Helix/lead angle

γ = arctan z1/q

The configuration details for this step can be found in the installation guide.

Normal tooth pitch

Axial tooth pitch

px = πx



Basic tooth pitch

Lead

pz = z1 px



Virtual/alternate number of teeth

Helix angle at basic cylinder

sin γb = sin γ cos αn



Worm pitch cylinder diameter

Worm gear pitch circle diameter

d2 = z2 mx



Worm outside cylinder diameter

Worm gear outside circle diameter

da2 = d2 + 2m (ha* + x)



Worm root cylinder diameter

Worm gear root circle diameter


WORM GEAR DESIGN PDF

df2 = d2 - 2m (ha* + c* - x)



Worm rolling(work) circle diameter

Worm gear rolling(work) circle diameter

dw2 = d2




FREE WORM GEAR CALCULATOR

Worm gear root circle diameter

Center distance

Chamfer angle of worm gear rim

Worm tooth thickness in normal plane

Worm gear tooth thickness in normal plane

Worm tooth thickness in axis plane

sx1 = s1 / cos γ



Worm gear tooth thickness in axis plane

Work face width

bw = min (b1, b2)




WORM GEAR RATIO CALCULATOR

Contact ratio

εγ = εα + εβ

where:


WORM GEAR DESIGN CALCULATION PDF DOWNLOAD

Minimum worm gear tooth correction

where:


WORM GEAR CALCULATION FORMULA

ha*0 = ha* + c* - rf* (1 - sin α)

c = 0.3

for α = 20 degrees

c = 0.2

for α = 15 degrees




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