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. Input Parameters Teeth type - common or spiral Gear ratio and tooth numbers Pressure angle (the angle of tool profile) α Module m (With ANSI - English units, enter tooth pitch p = π m) Unit addendum ha. Unit clearance c. Unit dedendum fillet r f. Face widths b 1, b 2 Unit worm gear correction x Worm size can be specified using the: worm diameter factor q helix direction γ pitch diameter.
  1. Worm Gear Design Calculation Pdf Download
  2. Worm Gear Design Calculation Pdf Template
  3. Worm Gear Design Formula
  4. Worm Gear Calculation Formula

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:

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

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

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

N1/N2 = T2/T1

And, we will get:

T2 = 5 * T1……………….Eqn.1

T1 + T2 > 40………………Eqn.2

T1 = 7 andT2 = 35

D1 = 2.4 P + 1.1

= 16.0712 mm

D2 = T2*P/3.14

= 69.53185 mm

C = (D1 + D2)/2

= 42.80152 mm

(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 Gear Design Calculation Pdf Download

Worm size can be specified using the:
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
Gear
px = πx

Worm Gear Design Calculation Pdf Template

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

Worm Gear Design Formula

Worm rolling(work) circle diameter
Worm gear rolling(work) circle diameter
dw2 = d2
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)
Contact ratio
εγ = εα + εβ
where:
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