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. 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.

To calculate a worm gear with center distance 100 mm. The worm has 2 teeth, and the worm wheel has 41 teeth. The axial/transverse module is 4. The pressure angle at the normal section is 20°. The worm's facewidth is 60 mm. You should select a sensible facewidth for the worm wheel. The axis tolerance is js7.

ZAR3 Worm Gear Calculation ZAR3+ Software for Cylindrical Worm Gear Design (C) Copyright 1993-2017 by HEXAGON Software, Berlin Bases for Calculation ZAR3 calculates all dimensions of cylindrical worm gear pairs with ZI, ZA, ZK, ZN or ZH worms, as well as efficiency, tooth forces and the safety margins against root fatigue fracture and pitting. Pre-dimensioning In pre-dimensioning recommendations are made for axial distance, modulus and number of teeth based on gear ratio, drive power, drive rotational speed and material. The recommendations can be used in the following geometry and strength calculations. Geometry Calculation In dimensioning you can adjust the recommended values to match available sizes or company standards. Or by varying the axial distance ratio and addendum modification you can determine the optimum worm gear for your application.

Strength Calculation The strength calculation computes the factors SF (fatigue fracture) and SH (pitting) along with tooth forces on the worm and worm gear, as well as the efficiency of the gear. Efficiency ZAR3 calculates the toothing efficiency, toothing and idling loss of power. The program provides recommended values and help graphics for determination of the tooth friction value. Material Data Base The program already includes a data base containing the most important gear materials and their values.

Users of the ZAR1+ spur gear and ZAR2 bevel gear programs can access this as a common data base. Tooth Forces Axial and radial forces, as well as tangential force and normal force are calculated. These values can be transfered to the WL1/WL1+ software for shaft calculation. Plus-Version ZAR3+ The extended version ZAR3+ provides additional functions: ZAR3+ generates true-scale drawing of worm and worm gear.

ZAR3+ provides an additional input window for modifications of tooth height factors and profile shift coefficient x. These functions are useful for design of complementary gears of steel worm and plastic worm gear. ZAR3+ calculates tooth thickness and over pin/ball diameters (OPD). You can enter pin diameter and flank tolerances or select from tolerance system according to DIN 3967.

CAD Interface A true-scale drawing of worm and worm wheel, as well as tables with the gear data can be exported to CAD via the DXF or IGES interfaces. The drawings can of course also be displayed on screen and printed out. Import/Export Text printout can be generated as HTML table and exported to Excel. Input data may be loaded from an Excel worksheet.

HEXAGON Help System For all entries a help text or auxiliary picture can be displayed. For example, there are diagrams for input of the tooth friction value µz0 in relation to lubricant and average slide speed. There are also diagrams for optimizing the diameter-to-center distance ratio dm1/a in relation to fatigue stress or efficiency. Users can modify and append help texts and auxiliary pictures. When error messages occur you can have an error description and remedy suggestion displayed.

Hardware and Software Requirements ZAR3+ is available as 32 bit and 64 bit application for Windows 7, Windows 8, Windows 10. Scope of Delivery CD-ROM or zip file for download with program and pdf manual, License agreement for indefinite period of time. Information and Update Service HEXAGON Software is continuously improved and updated. Licensed users can obtain new versions at the update price.

Worm Gear Design Calculation Pdf Files Pdf

Each program is provided with an individual license number and user files. No extra charge is made to registered users for telephonic support and hotline use.

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

Worm Gear Design Calculation Pdf Template

• 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

Worm Gear Design Calculator

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

Spiral gearing ZA

Axial module

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

d₂ = z₂ m_x

Worm outside cylinder diameter

Worm Gear Design Calculation Pdf Example

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 Ratio Calculator

Worm gear rolling(work) circle diameter

d_w2 = 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

s_x1 = s₁ / cos γ

Worm gear tooth thickness in axis plane

Work face width

b_w = min (b₁, b₂)

Contact ratio

Worm Gear Design Formula

ε_γ = ε_α + ε_β

where:

Minimum worm gear tooth correction

where:

Worm Gear Ratio Formula

h_a^*₀ = h_a^* + c^* - r_f^* (1 - sin α)