Worm Gear Design Calculation Pdf

Posted on 16-09-2021 by admin

Worm Gear Design Calculator
Worm Gear Design Calculation Pdf Download
Worm Gear Design Calculation Pdf Example
Worm Gear Ratio Formula
Worm Gear Ratio Calculator

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

Worm Gears Common to specify lead angle lfor worm and helix angle G for gear. Common to specify axial pitch p x for worm and transverse circular pitch p t for gear. Pitch diameter of gear is measured on plane containing worm axis Shigley’s Mechanical Engineering Design Fig.
Gear Ratio BJ-worm gears are available with the following nominal gear ratios: Dimensioning Gear Size and Gear Ratio By using the graphs on subsequent pages, you can dimension gear size, gear ratio and number of revolutions as well as motor according to your requirement. Alternatively, you can use the tables on pages 27 to 29.

D2 – Pitch Diameter of Gear

In worm gear drives, a tribological calculation method has been developed at the Institute of Machine Elements, Gears, and Transmissions (MEGT), University of Kaiserslautern (Ref.1).This simplified tribological model of the tooth mesh-ing by worm gears is shown in Figure 2.

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 r_f^*

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

m_n = m
Normal module	m_x = m_n cos γ
Axial pressure angle	α_x = a
Normal pressure angle	α_n = arctg (tg α cos γ)
Helix/lead angle	γ = arcsin z₁/q

Spiral gearing ZA

Axial module

m_n = m_x / cos γ
Normal module	m_x = m
Axial pressure angle	α_n = arctg (tg α cos γ)
Normal pressure angle	α_x = 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

p_x = π_x

Basic tooth pitch

Lead

p_z = z₁ p_x

Virtual/alternate number of teeth

Helix angle at basic cylinder

sin γ_b = sin γ cos α_n

Worm pitch cylinder diameter

Worm gear pitch circle diameter

Worm Gear Design Calculator

d₂ = z₂ m_x

Worm outside cylinder diameter

Worm gear outside circle diameter

d_a2 = d₂ + 2m (h_a^* + x)

Worm root cylinder diameter

Worm gear root circle diameter

d_f2 = d₂ - 2m (h_a^* + c^* - x)

Worm rolling(work) circle diameter

Worm gear rolling(work) circle diameter

d_w2 = d₂