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Z A R 3 +

Software for Worm Gear Design

(C) Copyright 1993-2024 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.


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.


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.

Tooth Forces

Axial and radial forces, as well as tangential force and normal force are calculated. These values can be transfered to the WL1+ software for shaft calculation.

Plus Functions of ZAR3+

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.


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 z0 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 11, Windows 10, Windows 7.

Scope of Delivery

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

Download ZAR3+ Demo for Windows (740 kB)

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